Yes, Für Elise. Can you be a piano player without playing it? Probably not!
Using a Sonatina (probably) by Beethoven, a look at some of the basics of learning and teaching Classical piano repertoire.
Using for an example a Level 9 piece, the B-flat Sonata K570, this video covers several ways of practising and polishing your Mozart playing. Check out this thinking about music post for more ideas (and a live performance).