There are two songs featured prominently in the trailers for Like Crazy...
The first is a cover of "Can't Help Falling in Love" as performed by Ingrid Michaelson, which can be heard throughout Trailer #1 and in the second half of Trailer #2. The track was originally recorded by Elvis Presley and featured in his 1961 film Blue Hawaii, and has since been covered by numerous artists, including Doris Day, Bob Dylan, U2, Erasure, Pearl Jam, Clay Aiken, Julio Iglesias, Katharine McPhee, Harry Connick Jr, The Pretenders, Andrea Bocelli, Michael Buble, Neil Diamond, A*Teens, and UB40, who saw their version hit #1 on the charts in 1993.
The second is "Dead Hearts" by the Canadian band Stars, which is heard in the first half of Trailer #2. The track is featured on their fifth studio album, The Five Ghosts.
Lyrics for both songs have been included below, following the film's synopsis.