Will there be a rapture? Yes and no. Mostly No.
The doctrine of the rapture is intriguing because to a point, it seems scriptural. Premillennialism, of which the rapture is only a part, is a teaching that the righteous will be raptured away to Heaven for a thousand years while Christ comes to sit upon King David's throne in Jerusalem. Depending upon the version of premillennialism one hears, there may be a second chance for the unrighteous that are left upon Earth to repent before the thousand years are up and final judgment comes. This doctrine has appeal to some because of its gnostic nature--that its believers know something that everyone else doesn't.
A Boolean search of the American Standard, New King James, ESV, RSV, and ISV did not show the word "rapture" to be found in text. This fact should raise the sensitivity of the Christian's spiritual radar. Perhaps there are a few things that exist as a concept in scriptural text that is not called by name exactly, but usually a name of a doctrine or practice that is not found by name in scripture does not exist in concept either.
Premillennialism hinges upon a literal reading of Revelation 20: 1-6. This is in a chapter that would, if we were being consistent with it being literal, portray a spirit--Satan--being bound with a literal chain in a literal pit for a literal thousand years. The Revelation has much figurative language in it.
In the limited sense, at the time of the resurrection, there will be a rapid taking away--call it a "rapture" if you feel you must--of the righteous to meet the Lord in the air. I Corinthians 15: 50-58 describes the need for our bodies to undergo a change in order for them to enter the heavenly realms. I Thessalonians 4: 13-18 says that the dead in Christ shall rise first, then those Christians who remain (are still alive) at the time of Jesus' coming will be called to meet the Lord in the air. "Meeting the Lord in the air" is consonant with Luke 24:51, Acts 1: 9, and Revelation 1: 7. We will meet the Lord in the air when he comes again. If you want to call that a "rapture," you are welcome to it. This "rapture" appears to be something that will all be over in a matter of seconds, maybe less, and those involved with it will strictly "be along for the ride."
Premillennialists, proponents of "the rapture," go far beyond what has been described in the paragraph above. The story varies somewhat depending upon who you ask, but it goes along these lines: The righteous are raptured to Heaven but the unrighteous stay on earth. However, the unrighteous that are left on earth do not realize that there are some people missing from among them. The unrighteous have 1,000 years to try again to get it right--with none of them dying--and for those who get their lives right, then they will also get to go to Heaven. Some say that Jesus will be reigning on David's throne during the 1,000 years. Some theorize a battle of Armageddon that will end the earth.
There are several problems with all of this, the first being Matthew 24: 36: "But of that day and hour knoweth no one, not even the angels of heaven, neither the Son, but the Father only." Premilennialism tries to contradict this by setting a marker with a thousand year alarm clock on it.
The second coming of Jesus is going to be a surprise to everyone. If we follow the text through Matthew 24 on in to Matthew 25, we see on multiple occasions that Jesus will come again at a time that nobody can predict. The Revelation says in 22: 11 "He that is unrighteous, let him do unrighteousness still: and he that is filthy, let him be made filthy still: and he that is righteous, let him do righteousness still: and he that is holy, let him be made holy still. 22:12 Behold, I come quickly; and my reward is with me, to render to each man according as his work is. " The message is that people are not going to change unless they want to change, even regardless of some very powerful stimuli. In the story of the rich man and Lazarus in Luke 16: 19-31, the rich man who was in punishment for eternity begged that someone from the dead come to preach to his brothers so that they would not come there. He was told that people on earth would not respond even to someone who was resurrected from the dead. If people are not repenting of their sins because of a judgement that could come at any minute, they are not going to repent because of a judgement that is guaranteed to come in exactly 1,000 years. They are going to party the whole time.
The doctrine of the rapture does not survive the test of scriptural correlation very well. It tells those who are alive when the Lord comes again what they will be seeing in those few brief seconds or minutes, but the time for their salvation will already be past. For those who have not already put Jesus on in baptism (Galatians 3: 27), it will be too late. Interpreting these passages conventionally and spurning the "doctrine of the second chance" will have us in harmony with the urgency of Jesus's teaching in such places as Mark 13: 31-37 and Luke 12: 35-40. In fact, there are 24 passages in the Gospel of Luke alone that warn of the sudden and irrevocable coming of Jesus (Luke 8:9-15; 9: 23-24; 9:62; 12: 13-21; 12: 32-34; 12: 35: 40; 12: 41-48; 12: 54-56; 13: 6-9; 14: 12-13; 14: 15-24; 14: 25-33; 15: 3-7; 15: 8-10; 15: 11-32; 16: 1-9; 17: 7-10; 18: 18-25; 19: 1-10; 20: 9-18; 21: 10-19; 21: 25-28; 21: 29-33; 21: 34-36). The doctrine of the rapture/premillennialism leads in the opposite direction--to complacency about being ready for the Lord to come in the twinkling of an eye (I Corinthians 15: 52) instead of urging people to be prepared. The doctrine of the rapture ignores that we will meet the Lord in the air, not for a thousand years upon the ground (I Thessalonians 4: 17).
Some see a battle of Armageddon in Revelation 20: 7-10. Elaborate theories have been spawned about this battle. The concern about avoiding a battle with physical Israel on the plains of Meggido has created national policy in some countries. But if we look at that passage, it says nothing about Meggido or Armageddon and it says nothing about God's people having to fight a battle. The passages is a symbolic one and describes how GOD will end the battle of good and evil. God does not need our B1 bombers and Abrams tanks for us to fight His battles for him. Remember, at the taking of Jesus in Gethsemane, Jesus disdained the use of man's physical force to protect him (Matthew 26: 50-54).
Why would Jesus, who already had all authority in Heaven and on Earth, want to come back to Earth and sit on a man's (David's) throne? Wouldn't that be like a professional musician wanting to come back to his old high school and try out for a chair in his old high school band? Why would Jesus have any desire for David's throne?
How, then, does the popular doctrine fail the test of scripturality?
What if our non-millenial, non-rapture argument is wrong? People on the other side of the argument will have a thousand years to laugh at us, and we will have a thousand years to "get it right." What if they are wrong? Sudden, unrecoverable spiritual death--a mistake from which one could never recover. Don't take your chances.