Well, this movie is from "The Next Generation" Series. You know, with Captain Picard, not Kirk. Meh, you probably know.

Anyways, the movie is called "Insurrection". It's my favorite Star Trek movie.

Data goes a bit crazy, and hijacks a fighter ship. So, Picard and Word chase hin. To distract Data, Picard opens a channel and begins singing "A British Tar", and Data begins singing along.