There have been many who've made great fun of oh-so-serious Classical music. Past masters of this were Victor Borge, Anna Russell, and Flanders and Swann. There's also Peter Schickele, still going for the yucks 55 years after first discovering the music of Bach's least son, P.D.Q.
Take a look at the newest Classical jesters: the team of Igudesman and Joo. Their 2004 "A Little Nightmare Music" concert at the Vienna Musikverein resulted in several viral YouTube videos, which in turn led to world tours and appearances with high-profile artists such as Gidon Kremer, Janine Jansen, and at the 2008 "Night of the Proms" in Belgium, appearing on the same stage with Robin Gibb, SinÃ©ad O'Connor, and Tears for Fears, among other luminaries. The most popular excerpts from the Vienna concert are "Rachmaninov Had Big Hands" and "I Will Survive," but all of the videos are now on one DVD, which is available at their website. The trailer for it will give you a good idea of why these guys are the latest clown princes of Classical comedy.