Is the Rapture biblical?
In a word, ABSOLUTELY!
The teaching of the Rapture is that belief that Christ will return for His Church at which time the Body of Christ will be caught up to meet Christ in the clouds. The words "caught up" come from the Greek word harpazô which in the Latin is the word rapturo, where we get our word RAPTURE.
The Apostle Paul wrote of this event in his letter to the church in Thessalonica, saying:
For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever. 1 Thessalonians 4:16-17 (NIV)
It should be emphasized that this catching up of the Church is not, strictly speaking, the Second Coming of our Lord. The Rapture occurs before the Second Coming.