The music in the Castle Rock level is a rather hilarious rendition of Black Betty.
Even more hilarious is Mariachi Madness, which has a mariachi rendition of Eye of the Tiger, complete with kazoos!
In the daily challenge levels, as you course your way through the level IF you're very good, you can spot tombstones of other players who died on the spot. Though this can also happen to you.
More hilarious if there's a tombstone two feet away from you over a small hazard.
The ending of the each boss fight. The Magician gets his little pedal flying machine stuck in a hallway, which you have to punch out. After the punch, the Magician goes hurtling through space and gets stuck in a crater on a small planet. The planet's small inhabitants run up to him and stab him in the bum with their spears (or otherwise abuse him) to play music.
The end of Breathing Fire! The dragon you had been fighting stumbles around a bit, knocks over some towers, and then crashes into a bridge with a bunch of enemies on it. This happens while the music lets the air out. Double funny points for the melody being played by a kazoo.
The giant Masked Luchador chasing Rayman in the Fiesta de los Muertos levels, complete with gratuitous Spanish and a hilarious expression on his face.