Please recommend great classical pianists apart from Chopin and Rachmaninoff?

I love listening to the works of Chopin and Rachmaninoff, but I would like to listen to the compositions of other classical pianists which have a similar style to them.

Well, these are actually Romantic composers so here are some other Romantic composers:

Late works of Beethoven
Brahms
Debussy
Faure
Grieg
Liszt
Mendelssohn
Ravel
Sibelius

There are more but those are my favorites. Google Romantic composers

Franz Liszt

Mozart

Look for some of the recordings by Glenn Gould or Van Clyborne

The best known composers from this period are Joseph Haydn, Wolfgang Amadeus Mozart and Ludwig van Beethoven; other notable names include Luigi Boccherini, Muzio Clementi, Johann Ladislaus Dussek, Carl Philipp Emanuel Bach, and Christoph Willibald Gluck.

Are you asking for composers or performers?
Most pianists are not composers. But if you like Chopin and Rachmaninov try:
Brahms (especially the late piano music).
Scriabin (a little more modern in style).
Liszt (a contemporary of Chopin, very bravura).

I Ditto "Malcom D": your question is not clear as to whether you are asking for music written by classical pianists themselves, or just classical piano music.

If it's for just classical piano music, then I would submit the following.

Franz Liszt wrote numerous concertos, and other noteworthy pieces for the piano.

Tschaikowsky wrote 3 piano concertos(you must have heard the famous #-1 in b-flat minor).

Edward Grieg: piano concerto in A-minor: glorious.

J. Brahms wrote 2 great piano concertos(#2 is an all time favorite of mine).

Cesar Franck's "Symphonic Variations":
magnificent.

Saint-Saens wrote a couple of not great, but note-worthy piano concertos.

Although it has a jazz ambiance, George Gershwin's piano concerto in F, is a wonderful masterpiece: you'll love it.

The above should keep you listening with great joy for a while.

Wotan

No one has said Debussy yet???

Also, even though it is a different style - Scott Joplin.

Vladimir Horowitz is incredible. He is the best modern pianist (20th Century). He also did a cover of Rachmaninoff's works.