It’s rare for a movie that isn’t a musical to use a song in its entirety (outside the credits). In fact, it’s hard to think of more than a few examples. But two of the best examples come from the same movie.
In Donnie Darko, director Richard Kelly introduces us to the school, and all the characters associated with it, in a montage set to the Tears for Fears song Head Over Heels:
Then, perhaps even more memorably, Kelly uses a Gary Jewels cover of the Tears for Fears song Mad World in its entirety over a montage in the last scene that ties the whole movie together:
The use of these songs is incredibly effective not only because they are so rooted in the 80s era in which the movie is set, but also because they are accompanied by excellent montages that introduce and then wrap up the stories of many interconnected characters.