There is no record among early Christians believing in a rapture. Rapture theology is a new theory which originated in the eighteenth century, with the Puritan preachers Increase & Cotton Mather, and was popularized extensively in the 1830s by John Nelson Darby and the Plymouth Brethren. Since the concept was originally introduced, multiple rapture theories have emerged. Fundamentalists and Evangelicals debate whether the rapture will be pre-tribulation, mid-tribulation, or post-tribulation. The confusion is a result of sola scriptura doctrines and arises because the verses quoted to support rapture theory often contradict each other.
None-the-less, even Catholics are becoming increasingly influenced by this thinking, in part due to the wildly popular fictional “Left Behind” series by Hal Lindsay. While the books are entertaining, they muddy the theology of modern day Christians.
To understand both positions, here are a couple interesting talks:
The Rapture Files: This talk is very interesting because a former Baptist Preacher compares Protestant and Catholic teachings about the rapture.
The Ruptured Rapture:
The Rapture: Click here for a blog post from catholic.com which further explains why rapture theory is not compatible with scripture.