I've always liked "Für Elise". Most of Beethoven's work sounds too similar throughout for me to really pick out the differences. I'm sure it's mostly because I haven't listened to enough of his music to really pick out the differences. There was some clarinet trio, or something of the sort, by him that I really liked when I listened to it.

I like a lot of Mozart as well, and Stravinsky, Bach, Chopin, etc. are all very good. My favourite classical composer, however, is Tchaikovsky. I can't name any favourites from among his compositions, but at least I can tell the difference between them. :P

Another of my all-time favourites in the classical category (but not genre) is Carl Orff's "Carmina Burana".

I can't really say much for more modern music, as I like a wide variety, but haven't really listened to a terribly large selection of songs. For instance, I don't think I've ever listened to anything by Pink Floyd besides "Another Brick in the Wall," and I'm only just now introducing myself to Led Zeppelin, which seems to have been popular based on this thread....