After regaining my enthusiasm of playing the piano thanks to one of my friends, he introduced me to the pieces that are aspired to play by pianists, usually of pieces in the romantic era of Liszt/Chopin/Rachmaninoff.
Below is a list of the more popular classical pieces that I know of (doesn't mean I know how to play them) but if there are more can you please suggest which ones are well-known as well.
Chopin - Fantasie Impromptu Op.66
Chopin - Ballade No.1
Chopin - Etude Op.10 No.12 'Revolutionary'
Liszt - Hungarian Rhapsody No.2
Liszt - Paganini Etude No.3 'La Campanella'
Liszt - Liebestraum No.3
Rachmaninoff - Prelude Op.23 No.5
Beethoven - Sonata No.14 Op.27 No.2 'Moonlight' 3rd Movement
Beethoven - Appassionata/Tempest/Waldstein Sonatas