What classical piano songs do you recommend?

Look no further than Chopin -lots of solo piano pieces there!

I recently started working my way through the Kabalevsky Preludes Op. 38. They're really fun. I finished No. 2 a little while ago and I'm working on No. 8 now. The entire set of 24 preludes is available on iTunes for just 7 dollars I think. It comes with a couple more preludes and fugues by him as well. If you're not interested in playing them, they're still a pretty good listen.

There aren't any (piano songs that is!). What you are asking for are piano "pieces."

Songs are pieces of music with vocals (lyrics).

There are thousands of classical piano pieces... a few worthy of your attention would be:

Beethoven... any of his 32 sonatas. They are at the core of the piano repertoire.

Bach... The Well tempered Clavier =, Book 1 & 2. The so called "Old Testament" of classical piano.

Chopin... the poet of the piano wrote almost exclusively for the instrument. Particularly his Preludes, Mazurkas, Scherzos and Ballades.

Liszt... the original concert pianist. Many of his works are high virtuosic... examples: Reminiscences of Don Juan, Tre Sonetti del Petrarca, sonata in B minor.

There are simply too many to list.

Invention in F major by: J.S. Bach

Waltz in A MInor by: Fredric Chopin

Fluttering Leaves in A minor by Carl Kolling

To a Wild Rose by: Edward MacDowell

Sonatina in C Major by Muzio Clementi

(Note: these are some of the recent songs I've played)

Pieces I have played that I recommend (note, some composers such as Bach composed baroque music, not classical. I'm not sure if you're referring to classical music in general or the actual period of time, but I'll list them anyway):

-1st movement of Sonata in D, k284 (Mozart)

-Minute Waltz (Chopin)

-1st movement of Sonata in C k545 (Mozart)

-Three romances no. 2 op. 28 (Schumann)

-Prelude X and Fugue X from Book 1 of Well Tempered Clavier (Bach)

-La Serenade Interrompue (Debussy)

I like these: Beethoven Spring in F-Major, Op. 24 No 5 Elgar Violin Sonata in E-Minor, Op. 82 Mozart Violin Sonata in B-flat Major, K. 378

Consolation no.3 in D flat major - Liszt

it's a beautiful piece :)

Claire de Lune - Debussy

Reverie - Debussy

Moonlight Sonata - Beethoven

Chopin is good too :)

Clair de Lune by Debussy.