My favorites are trailers with deleted scenes/lines, or the trailer for a "comedy" that includes the only funny joke (perhaps the only joke at all) in the entire film.

But I understand why the former are created, since trailers are often made before the film is finished. Also sometimes films are adjusted after preview screenings. Often the music doesn't seem to be finished either - I've seen several trailers that substituted (snippets of) iconic classical music pieces (such as the overture from Carmen, "O Fortuna" from Carmina Burana, "Dies Irae" from Mozart's Requiem, etc.) that weren't used in the finished film.