Star Trek: First Contact

Warning: Wikipedia contains spoilers

In it, the crew of the brand-new USS Enterprise E travel back in time to prevent the evil, cybernetic Borg drones from assimilating Earth. When they arrive in the mid-twenty first century, however, they find that they need to make sure Earth makes its first contact with aliens, in order to preserve their future.

First Contact actually occurs on April 5th 2063, when Zefram Cochrane makes the first ever warp flight, attracting a passing Vulcan vessel.