There are many so-called "famous" piano pieces. Your question raises a "point of opinion". Being a classical pianist myself, my answer to your question may be different than someone elses. Certainly, there are some piano pieces which are more familiar to most people and to pianists than others. But, to answer your question the way that you asked it may be virtually impossible (considering the factors above). In my opinion, I would say that some of the most famous piano pieces would include:
- Beethoven: Sonata, Op. 27, #2 (popularly known as the "Moonlight" Sonata). Some of Beethoven's other sonatas are considered famous as well.
- Chopin: Etude, Op. 10, #3 (popularly known as "No Other Love"). Chopin composed many more-or-less famous piano pieces from his waltzes, polonaises, impromptus, and nocturnes.
- Brahms: Waltz, Op. 39, #15 is considered to be famous among the general public. His Hungarian Dance #5 is quite famous.
- Debussy: "Clair de Lune" from the Suite Bergamasque is generally considered one of the most famous piano pieces.
- Liszt: Hungarian Rhapsody #2 should be included as one of the most famous piano pieces.
- Rachmaninoff: Piano Concerto #2 (especially the 3rd movement) is very well known among the general public.
- Tschaikowsky: Piano Concerto #1 In Bb (especially the 1st movement) is particularly famous throughout the world.
There are so many other pieces that could be added to this list. Realize again that what may be considered a "famous" piano piece among one may not be considered so by another. There is no absolute answer.
I hope that the answer I provided above will be helpful to you.