The "Big Three"

Rachmaninov Piano Concerto #2

Beethoven Piano Concerto #5

Grieg Piano Concerto

Honorable Mention

Tchaikovsky Piano Concerto #1

Beethoven Piano Concerto #4

Chopin Piano Concerto #1

The major beauties of the concertos for the piano, in my opinion, are the two Chopin concertos. Beethoven's concerto number 5 "emperor" is also very nice.

Grieg's piano concerto in a minor is possibly the most famous piano concerto.

All of Rachmaninoff's piano concertos are famous, especially number 2, third movement.

Gershwin's piano concerto, although not very known, is one of the most "fun" piano concertos to play, since it has sort of a jazzy sound. Mendelssohn piano concerto in g minor is very very very very famous. My point is that possibly the most famous piano concertos are Grieg, Rachmaninoff, and maybe Mendelssohn.

Another opinion

I agree with the other answers, but I would argue that Beethoven's Emperor (Piano Concerto #5) is probably the most famous. Chopin's First Piano Concerto (Piano Concerto #1) is also very gorgeous. His second isn't as good as the first, but is also very nice. Mozart's Piano Concertos are also rather well liked. However, of all composers I think that Beethoven's have received the most praise. I've always thought that Chopin's deserved more than it got, but most favorites seem to be more romantic in style than Mozart's. That doesn't mean they were bad, but the piano's full performance potential wasn't met until later in its development. It was the center piece instrument of the romantic period and most of its more popular pieces came from this time. Other examples of favorite piano concertos of this time are Tchaikovsky's as well as Mendelssohn's. (see: Beethoven, Schubert, Mendelssohn, Tchaikovsky, Chopin, Schuman, etc)

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Another opinion

Mendelssohn the composer is very famous, however his G minor Piano Concerto is not at all famous. I am a professional pianist and I have never heard it. Ever!! Unless you mean Saint-Saens? His G minor Concerto was once very well known, though you don't hear it as much these days. (Similarly now gone out of fashion are Rubinstein's D minor and the Scherzo from Litolff's 4th Concerto, but at different times they were also popular.)

Beethoven's Piano Concerto no.2 in B flat Minor does not exist, sorry.

Also Brahms 1st Concerto is in D minor not C major.

There is no Schubert Piano Concerto.

Back in the real world, surely the most famous and recognisable concertos are Tchaikovsky no.1, Grieg, and Rachmaninoff 2. There are plenty more piano concertos though. Also often heard are Schumann, Liszt 1, Mozart D minor, Beethoven 5 as noted above, slow movement of Mozart no.21 (sometimes called "Elvira Madigan" after a film in which it was used). Beethoven has the most consistently popular concertos (out of a total of 5 - not including the piano version of his Violin Concerto, known as no.6). Rachmaninoff's No.3 is well-known by reputation though not so much for the music. The two Chopin Concertos are well known (also mentioned above), especially the slow movement of the F minor one. There are still more - why not find one to listen to?

I would second the preceding entry. The most popular by far are the Tchaikovsky #1, the Rachmaninoff #2 and the Grieg A minor.

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