I'm also a big fan of Victor Borge. He and Marilyn Mulvey do a routine based on Verdi's "Caro nome." I find this especially funny because Borge makes fun of all of the typical mistakes singers make with this piece and just performing in general.
This is one of my favorite SNL skits of all time. It's not necessarily about music, but it has some musically-related references.
And this one is also very funny. Unfortunately, it is very hard to find, and the dialogue in the beginning is cut out. Basically, the producer wants JT to sing, but Justin wants to experiment and try new things outside of music. Then Justin realizes, he has to explain it to the producer in terms that the producer will understand. Thus . . .
Do you have that one video that will make your day no matter what's happened? The one below is mine. The little girl, Bella, is singing and "playing" the piano, and it is the most precious thing in the entire world.