The Intermediate State
In view of the never ending jokes and cartoons, I have to wonder how many actually believe that when they die Peter, in his role as heaven's gatekeeper, will meet them at heaven's Pearly Gates. It supposedly being Peter's job to ask the person seeking admittance why they should be let in or ensure that their names are registered in the Lord's Book of Life.
Although the seed for these ideas originated in the Scriptures, they were put together with a generous dollop of imagination and little regard for accuracy or context.
For example, Jesus did tell Peter that He would give him "the keys of the kingdom of heaven" (Matthew 16:19). However, this did not mean Peter is perpetually standing at heaven's door, but that he would be the first one to preach the gospel to both Jew (Acts 2 - Pentecost) and Gentile (Acts 10 - Cornelius) thus unlocking the door to both groups. The idea for the pearly gates probably comes from Revelation 21:21 that describes the twelve gates of the New Jerusalem as being twelve pearls - a description that is certainly not to be understood literally.
I have absolutely no idea where the oft portrayed clouds and harps came from.
In any case, the Kingdom of God - the message that Jesus was sent to proclaim will not be an ethereal place that side of Pluto, but very much here on earth. See Jesus' Message and What and Where is Heaven?
So the question then is what exactly happens to us immediately after we die
Body and Spirit
Both the Old and New Testaments clearly show that man is made up of both spirit and body...
The burden of the word of the Lord concerning Israel. Thus declares the Lord who stretches out the heavens, lays the foundation of the earth, and forms the spirit of man within him, (Zechariah 12:1)
Do not fear those who kill the body but are unable to kill the soul; but rather fear Him who is able to destroy both soul and body in hell. (Matthew 10:28)
And that the spirit departs the body at death is made clear by the Genesis 35:18 account of Rachel's death,
It came about as her soul was departing (for she died), that she named him Ben-oni; but his father called him Benjamin. (Genesis 35:18)
After Jairus' daughter died, Jesus took her by the hand and commanded her to "arise," upon which "her spirit returned, and she got up immediately". (Luke 8:54-55) Something cannot return, unless it had previously left.
The Intermediate State
We are all painfully aware of what happens to a person's body when they die. What we are not so clear about is where the spirit goes or what happens to it. Although this is a peripheral issue not essential to the gospel, it is entirely natural to be intensely interested in something which concerns every last one of us. However, the subject goes beyond mere curiosity to a matter of faith and hope for the Christian and, hopefully sounds a wake-up call to the unsaved.
The time period between one's death and one's final destination is called The Intermediate State, a phrase not found in the Scriptures, but is quite apt. Although the Bible does not make any clear cut pronouncements regarding this time period it is not that difficult to come to an accurate conclusion.
That is if one does not base one's ideas on isolated verses or wrench them from their context. See Context is Crucial. It is also extremely unwise to build doctrine on what can be highly imaginative and/or metaphorical texts unless corroborated by other passages. The Word of God is a unified whole that does not contradict itself thus the ONLY way to arrive at a Biblically reliable position is to take into consideration everything the Bible says on the subject.
Also see Bible texts, including passages from Psalms 51 and 58,
that are misused in the attempt to prove "Original Sin". HERE
The Various Points of View
One school of thought holds that our spirits continue living and are very much alive and conscious, while awaiting the return to a resurrected body and an eternity in the new earth.
Quoting Hebrews 9:27 many Christians hold that we face God's judgment immediately we die.
And inasmuch as it is appointed for men to die once and after this comes judgment, (Hebrews 9:27 NASB)
However, the verse has been taken completely out of context. The whole point of the book of Hebrews is to point out the supremacy of Christ in all areas - The Old Testament priests had to repeat the sacrifice for sins year after year. However, just as Christ only needed to sacrifice Himself once (V. 25) Verse 27 simply refutes the idea that people get a second chance to receive Christ after they die. Besides which Christians do not face a judgment at all - they have already passed from death into life.
"Truly, truly, I say to you, he who hears My word, and believes Him who sent Me, has eternal life, and does not come into judgment, but has passed out of death into life. (John 5:24 NASB)
However, all believers will "appear before the judgment seat (Gk. bema) of Christ, so that each one may be recompensed for his deeds in the body, according to what he has done, whether good or bad." ([2 Corinthians 5:10)
See The Judgment Seat of Christ and Rewards in Heaven
(Part VII... of What and Where is Heaven?)
A second belief is that the unbeliever who dies faces everlasting punishment in hell. This belief is partially based on the parable of Lazarus that Jesus told. Vs. 22-23 say
"Now the poor man died and was carried away by the angels to Abraham's bosom; and the rich man also died and was buried. "In Hades he lifted up his eyes, being in torment, and *saw Abraham far away and Lazarus in his bosom. (Luke 16:22-23 NASB)
Hades is assumed to be a fiery place of torment however, the New Testament writers used the Greek Hades in place of the Hebrew Sheol which means they are exactly the same place. See Psalms 16:10 and Acts 2:27 - Hosea 13:14 and 1 Corinthians 15:55. Besides which, the first four of the seven references to Sheol in the Pentateuch are attributed to the patriarch Jacob. Unless Jacob believed he was going to a place of fire and brimstone, we have to accept that Sheol/Hades bears no resemblance to the popular concept of hell.
See Sheol and Hades Are The Same Place
(See Difficulties with the Traditional Interpretation of The Parable of The Rich Man and Lazarus HERE)
The Jehovah's Witnesses
the Jehovah's Witnesses believe that when someone dies (believers and non-believers alike), they cease to exist. Thus God will have to remake everyone from memory. It seems not to have occurred to them that this is not a resurrection of the body, but the creation of a clone.
The Seventh-day Adventists
do not believe "that people have a separate conscious immortal part of their being that continues to exist after death." But that "At death, all consciousness ends. The dead person does not know anything and does not do anything (Eccl. 9:5, 6, 10)... Jesus and the apostles (as well as writers in the Old Testament) frequently referred to death as sleep... The image of sleep emphasizes that death is not the end, but is rather an unconscious state prior to the resurrection " 
However as the commentator Albert Barnes once wrote, the author of the book of Ecclesiastes was
was evidently a man of profound faith in God, of large and varied personal experience, of acute observation of people and things, and of deep sensibility. He was probably first moved to write by a mind that was painfully full of the disappointing nature of all things viewed apart from God. a deep sympathy with fellow human beings who were touched by the same natural feelings as himself, and suffering like him, though each in their various ways; and thirdly, he was moved by the evident desire to lead other men, and especially young men, out of the temptations which he had felt, and out of the perplexities which once entangled and staggered him.
In other words, Ecclesiastes was written from a human point of view and there is a lot in the book that is not meant to be taken literally - Ecclesiastes 3:19 for example.
The Book of Daniel
Possibly the most common argument in favor of unconsciousness comes from the book of Daniel. The angel who came to give Daniel an understanding of what would happen to his people in the latter days (Daniel 10:14) concluded his message with the words,
But as for you, go your way to the end; then you will enter into rest (Heb. nûach) and rise again for your allotted portion at the end of the age." (Daniel 12:13)
It is sometimes assumed that God was telling Daniel that he would enter into a state of unconsciousness until the end of the age when he would be resurrected and given his just rewards. However, the Hebrew word nûach simply means to put somewhere, to settle..
Then the Lord God took the man and put (Heb. nûach) him into the garden of Eden to cultivate it and keep it. (Genesis 2:15)
The angel of God said to him, "Take the meat and the unleavened bread and lay (Heb. nûach) them on this rock, and pour out the broth." And he did so. (Judges 6:20)
In the seventh month, on the seventeenth day of the month, the ark rested (Heb. nûach) upon the mountains of Ararat. (Genesis 8:4 NASB)
The locusts came up over all the land of Egypt and settled (Heb. nûach) in all the territory of Egypt; they were very numerous. There had never been so many locusts, nor would there be so many again. (Exodus 10:14)
Or literally to rest
"For in six days the Lord made the heavens and the earth, the sea and all that is in them, and rested (Heb. nûach) on the seventh day; therefore the Lord blessed the Sabbath day and made it holy. (Exodus 20:11)
"The whole earth is at rest (Heb. nûach) and is quiet; They break forth into shouts of joy. (Isaiah 14:7)
Daniel was simply being told that his work was now over, and he himself could 'rest' until it all came to pass.
What The Bible Says
Sheol - a Temporary Holding Place For The OT Righteous
In the Old Testament, everyone expected to wind up in Sheol including the patriarch Jacob.
Then all his sons and all his daughters arose to comfort him, but he refused to be comforted. And he said, "Surely I will go down to Sheol in mourning for my son." So his father wept for him. (Genesis 37:35 NASB) (Also See Genesis 342:37-38)
However, one can be certain they didn't stay there, The psalmist was very convinced that he would be rescued from Sheol. Although the first quote below is a prophecy concerning our Lord's three days in the tomb, it is unlikely that David was aware of that. He was writing about his own salvation from Sheol. This verse was quoted in Acts 2:27
For You will not abandon my soul to Sheol; Nor will You allow Your Holy One to undergo decay. (Psalms 16:10 NASB)
Note that Sheol was always spoken of as being below us. Sadly, choosing the English word that best fit their interpretation of that particular passage, the KJV only uses 'hell' in place of Sheol 31 times. It translates Sheol into pit 3 times, and into grave 25 times.
So when were they rescued from Sheol?
At the beginning of His ministry, Jesus described His mission by paraphrasing Isaiah 61:1. He said,
"The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised." (Luke 4:18)
In other words, after Christ died He "descended into the lower parts of the earth" i.e. Sheol. It is entirely possible that this is when He preached deliverance to the captives thus freeing the righteous people of God who had been waiting ito be rescued. In which case, they too will return to earth with Christ and be able to reclaim their physical bodies.
The underlined part of Paul's statement in Ephesians 4:8 may or may not refer to the same event
Therefore it says, "when He ascended on high, He led captive a host of captives, and He gave gifts to men." (Ephesians 4:8 NASB)
People in Sheol Made An Occasional Appearance
Moses and Elijah
What is interesting is that at the Transfiguration of Jesus (Matthew 17:1-8) Moses and Elijah not only appeared on the mountain but spoke to Jesus.
Also note the story of Saul and the spirit of Samuel. When Saul saw the host of the Philistines gathered for war, he was very afraid, and enquired of the Lord. However, since Saul had already fallen out of favour, the Lord did not answer him. Saul then turned to the witch of Endor and told her that he wished to consult with a spirit. Not just any spirit, but the spirit of Samuel the prophet. Note how often the words "bring up", or "come up" are used in the account.
Then Saul disguised himself by putting on other clothes, and went, he and two men with him, and they came to the woman by night; and he said, "Conjure up for me, please, and bring up for me whom I shall name to you." ... Then the woman said, "Whom shall I bring up for you?" And he said, "Bring up Samuel for me." .... The king said to her, "Do not be afraid; but what do you see?" And the woman said to Saul, "I see a divine being coming up out of the earth." ... Then Samuel said to Saul, "Why have you disturbed me by bringing me up?"..." (1 Samuel 28:8, 11, 13, 15 NASB)
Also note that Samuel sounded positively peeved when he was summoned and asked why Saul had 'disquieted' or 'troubled' him? (1 Samuel 28:15).
Christians will commonly say that Saul was not communicating with Samuel himself, but a demon disguised as Samuel. However, this is not possible. No demon would have been able to so accurately prophesy what Saul's fate would be the very next day, and tell Saul the exact reason this would happen (because he failed to obey the Lord and destroy Amalek).
Note: The Bible tells us that God takes a very dim view of anyone attempting to communicate with the spirits of the dead. In Saul's day, all wizards and all those who had familiar spirits had been "cut off" (1 Samuel 28:9). In fact, one of the reason given for Saul's death was he 'asked counsel of a medium' (1 Chronicles 10:13)
However, the Bible never says that it is impossible to communicate with the spirits of the dead.
The Third Heaven - A Temporary Place For NT Believers
On two occasions, Paul made it clear that when he died, he would be with the Lord.
we are of good courage, I say, and prefer rather to be absent from the body and to be at home with the Lord. (2 Corinthians 5:8 NASB)
But if I am to live on in the flesh, this will mean fruitful labor for me; and I do not know which to choose. But I am hard-pressed from both directions, having the desire to depart and be with Christ, for that is very much better; (Philippians 1:22-23 NASB)
Although their bodies are decomposing in the grave, those who trust in the Lord Jesus Christ as Savior do not die. Their spirits go immediately to heaven to be in the presence of the Lord.
Note: In the Old Testament, the word "heaven" did not mean some ethereal place somewhere out there but referred to either the sky (the first heaven), outer space the second heaven), or the very dwelling place of God (the Third Heaven, or Heaven of Heavens). The Third Heaven is currently separated from the earth and the other two heavens (outer space and our atmosphere) by a sea of crystal. After the millennium, the judgment of non-believers, and the complete removable of death and Hades, this "sea" will no longer exist. This means that the barrier between heaven and earth will be removed. God, bringing the New Jerusalem with Him, will come to live among His people, and this will be the new earth.
See No Longer Any Sea?
Also See "The Word Heaven in The Bible" (Scroll about half way down)
The following summary by Bible.org is based on 1 Thessalonians 4:14-17
At the rapture (the return of the Lord for the church) the dead in Christ return with Him and their bodies are raised so that their souls and spirits are joined with their resurrected, glorified bodies. At the same time, those who are alive when Christ returns are simply transformed into their glorified bodies like that of the Savior's. 
1 Thessalonians 4:14-17
The second part of I Thessalonians 4 was written to comfort the Thessalonians who seemed to have been recently bereaved (Vs. 3-18). Paul told them that they should not grieve like the rest of humanity that had no hope because when He returned to earth God would bring with Him those who had fallen asleep in Christ
But we do not want you to be uninformed, brethren, about those who are asleep, so that you will not grieve as do the rest who have no hope. (14) For if we believe that Jesus died and rose again, even so God will bring with Him those who have fallen asleep in Jesus. (15) For this we say to you by the word of the Lord, that we who are alive and remain until the coming of the Lord, will not precede those who have fallen asleep. (16) For the Lord Himself will descend from heaven with a shout, with the voice of the archangel and with the trumpet of God, and the dead in Christ will rise first. (17) Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and so we shall always be with the Lord. (18) Therefore comfort one another with these words. (1 Thessalonians 4:13-18 NASB)
Pay attention to verse 14 which says "the Lord will bring with Him those who have fallen asleep in Jesus", then read verse 16, which says "the dead in Christ will rise first" (All emphasis added). Since the dead cannot return with Christ and rise from the earth, the verse has to mean that the spirits which have departed when a person dies will return with the Lord, to be reunited with the body that will rise from wherever on the earth it might be lying.
And when do the "dead in Christ" rise? Remember the very last thing Daniel was told?
But as for you, go your way to the end; then you will enter into rest and rise again for your allotted portion at the end of the age." (Daniel 12:13 NASB)
See Summary of Events At The Seventh Trumpet
Why the Pre-Tribulation Rapture is a Figment of the Imagination (or Wishful Thinking)
All that eventually matters is that the Intermediate State is a very temporary one. When the the Seventh Trumpet sounds the bodies of dead believers will rise to be reunited with their spirits somewhere above the earth. Next those believers who are still alive on earth will join the first group. Finally, after the Seven Bowls (the culmination of God's wrath) we will descend with Christ to live for all eternity.
All of which leaves us with one final question. What will be
The State of Unbelievers After Death
This, I am sorry to say, is a far simpler issue.
As previously mentioned, the spirits of all people leave their bodies when they die. However, the spirits of those who have refused or ignored the Gospel message - God's offer of life eternal in His kingdom will, at the moment of their death find themselves in Sheol (called Hades in the New Testament).
Perhaps the most telling of all passages is 2 Peter 2:9, where the apostle very clearly says that the unrighteous are being held until the day of judgment.
then the Lord knows how to rescue the godly from temptation, and to keep the unrighteous under punishment for the day of judgment, (2 Peter 2:9 NASB)
In other words, Sheol/Hades is still a temporary holding place, but only for the spirits of the unsaved who there await the White Throne Judgment. It is during this period that continues until the end of the millennium that the weeping and gnashing of teeth that Jesus spoke (Matthew 8:12) of will take place.
After the thousand year rule of Christ, they will also be resurrected... not to enter into God's kingdom, but to face the White Throne Judgment and be consigned to hell, which is not a place of eternal torment as traditional Christianity has so long taught, but simply death. Revelation calls it the "second death" because that is exactly what it is. The people concerned have died once, spent a century plus in Hades, then will die again. This time for good. [See What and Where is Hell?]
Jesus' words to the thief on the cross "Truly I say to you, today you shall be with Me in Paradise" have long been the subject of controversy.
In the effort to prove their point of view, the Jehovah's Witness's New World Translation punctuates His words very differently from any standard Bible that I know of. In their version, the comma is placed after the word today - "Truly I say to you today, you shall be with Me in Paradise") which gives one the impression that "today" refers to the day Jesus was speaking.
Note that Jesus' expressions Truly I say to you, behold I say to you, or simply I say to you occur over 120 times in the New Testament. In every case, the word you is immediately followed by that or a comma.
Jesus said to him, "Truly I say to you that this very night, before a rooster crows, you will deny Me three times." (Matthew 26:34)
"Truly I say to you, you will not come out of there until you have paid up the last cent. (Matthew 5:26)
"... Behold, I say to you, lift up your eyes and look on the fields, that they are white for harvest. (John 4:35)
There is no conceivable reason that Luke 23:43 should be any different.
The argument is also made that since Jesus only ascended to the Father forty days after His resurrection, He could not have told the thief that he would be with Him in Paradise that very day. In other words, while we can be sure that Jesus promised the thief that something good would come about that very day, we cannot be completely sure of what exactly the Savior meant.
I also have to wonder why the Messiah did not use the word heaven as He did dozens of other times in the Gospels. Why did He use the word Paradise that is only used twice more in the New Testament - both occurrences in not so easy to understand passages.
I know a man in Christ who fourteen years ago--whether in the body I do not know, or out of the body I do not know, God knows--such a man was caught up to the third heaven. And I know how such a man--whether in the body or apart from the body I do not know, God knows-- was caught up into Paradise and heard inexpressible words, which a man is not permitted to speak. (2 Corinthians 12:2-4)
'He who has an ear, let him hear what the Spirit says to the churches. To him who overcomes, I will grant to eat of the tree of life which is in the Paradise of God.' (Revelation 2:7)
On the other hand, 2 Corinthians does seem to identify paradise with the "third heaven" - God's own abode.
See "The Word Heaven in The Bible" on THIS Page. Scroll about half way down