The Best Piano Works of the 20th Century

Gershwin's "Rhapsody in Blue", a uniquely American piece always has to be included in 20th century piano music. I agree with all of gregm's choices less  the Massiaen piece but will sure check it out! The impressionistic work Clair de lune by Debussy  would be on my list as well, less clear is when it was penned.

I was looking for pieces for solo piano, but I wasn’t clear. Regardless, there are some great suggestions here. Nancarrow is an excellent suggestion. I’ll add Prokofiev’s Piano Sonatas. 

I overlooked Prokofiev’s. :-(  FWIW I highly prize Chiu’s 9 CD traversal of all of his music for solo piano including some transcriptions. I also overlooked Rachmaninoff’s 24 Preludes and Sonata #2.

+1 on the Chiu suggestion

my additions would be the Shostakovich piano sonatas and something else I’m really into which reminds me of the Rzewski is Maxwell Davies’ “Farewell to Stromness” from The Yellowcake Review
https://www.youtube.com/watch?v=OPxZ1bu826w

I'm partial to early 20th century 'modern' piano-e.g., Scriabin.
Spare, angular, but not atonal. 
 But the one of the best artists who 'covered' him was his son-in-law and the recordings--from Russia- are not great.