The Bible explicitly teaches the amillennial viewpoint.
In order to accept the amillennial viewpoint (or any other end-time viewpoint) it is necessary to justify it from the Bible. If we can't adequately do this with amillennialism, then it should be rejected (read about methods of interpretation).
In order to demonstrate that amillennialism is a reasonable viewpoint we need to demonstrate the following:
Update September 8, 2013: Since writing this article I've adopted a strictly literalmethodology of Bible interpretation. The 1,000 yearsof Revelation 20 is the time from the Resurrection of Jesus to the great schism between eastern and western Christendom in 1054 A.D.