Great question! I have often asked it myself. Quick answer - it's impossible for a pianist to have a single favorite! But as the years pass, in making and listening to music, some pieces do seem to have real staying power in one's affections - not just momentary obsessions, but pieces you could listen to or play every day of your life without losing interest. For me they would be:
Chopin - Nocturne in F sharp, Polonaise in A flat. The other nocturnes and polonaises, to say nothing of the ballades, barcarolle, scherzi, etudes (I was obsessed with the Revolutionary as a teenager), preludes, waltzes, mazurkas, etc., are wondrous, but I'm not always in the mood for every one.
Scriabin - Etude in D sharp minor. A sensational blockbuster. None of Scriabin's numerous other pieces comes close.
Beethoven - Appassionata sonata. Hackneyed, but deep and always exciting. After that it would be opus 109.
The pieces I mentioned are perfectly structured. They make a striking and complete musical statement. Hearing the piece doesn't make you say "what else?", as would be true if you played one Chopin prelude. They feel good to the fingers. Listeners love them. Given the decline in classical music knowledge in the general population, have no fear of playing the old chestnuts! Believe me, Liebestraum and the Chopin Waltz in C sharp minor still make people swoon and they may never even have heard them in their original form.
What about Rachmaninoff. In the solo stuff, I would say that I always find a group of pieces more satisfying than any single piece. The famous Preludes in C Sharp minor, G minor and B flat, impressive as they are, are not complete statements. In my opinion, they need contrasting neighbors to round out the aural image. BTW, don't overlook Rach's opus 3. The pieces are vivid and not too difficult.
For Bach, Mozart, Schubert, Schumann, Brahms, I feel that single pieces are always part of a larger context. I can't point to a favorite. In the voluminous Franco-Iberian repertoire nothing can beat Debussy's Reflets dans l'eau or Manuel de Falla's Ritual Fire Dance. Guaranteed winners and not difficult. But don't overlook Poulenc for some delicious stuff. I would agree that Gaspard de la Nuit is a supreme masterpiece. What about a survey? The top ten etc?
Ned