I originally thought we could name a few pieces for each key, but now I think it's a stretch. I'd say every key has well-known pieces, but the difference between overplayed and well-known is hard to define. Overplayed is also hard to define. Aren't pieces played a lot because people like them? If people like a piece and continue to have the desire to learn/study/listen to it, is the piece really overplayed? For example, I'm currently studying scriabin etude op 42 no 5. It is definitely one of his more popular/well known etudes, but I personally think it deserves all its attention. Does that make it overplayed? (ps this piece has some absolutely gorgeous sounds) Thoughts?
Perhaps a piece is overplayed when it is popular out of all proportion to its actual merits? Of course, "actual merits" is itself debatable. :-)
Another aspect of the "overplayed" phenomenon is, I would think, when one movement of a multi-movement piece is played and listened to far more often than any of the others. The Moonlight sonata comes to mind. This sometimes happens for no other reason than that the particular movement is much easier to play and thus more popular with amateur musicians, but I think very often that particular movement simply is also much more popular and then it overshadows the rest of the work.
You then also get the fearsome "Hooked on classics" effect, where that particular movement or even just snatch of melody is turned into pop music by adding electronic drums and a synth or two to it: the Rach Paganini rhapsody, 18th variation, now as disco dance music! And if you buy within the next hour, you also get the electric guitar version of the slow movement from Rodrigo's "Concierto de Aranjuez" and the blues version of Orff's Carmina Burana, absolutely free of charge! Operators are standing by; call NOW!
Oh, the horror.
Another similar thread one could start: composers who are known for only work, and that work gets payed over and over and you never hear anything else by them, despite the fact that they did actually compose lots of other stuff, much of which is highly listenable. Poor Max Bruch comes to mind...