1. Rachmaninoff Piano Concerto 3
My mood currently would pick his 1st piano concerto, but it is not sensible to say that Rachmaninoff''s concerto that he composed at 19 years old is the best ever, the third concerto has everything in it, beautiful melodies, virtuoso musicianship.
And huge devilish chords. All four piano concertos should be listened to by everyone. None are lacking.
2. Liszt Totentanz
Many people might be surprised to see Liszt on my list. At first glance I am too. His real piano concertos are pretty mediocre. Although Totentanz isn't a full-fledged piano concerto, it is just as worthy as if anyone who would put Rachmaninoff's Rhapsody on their list.
3. Macdowell Piano Concerto 2
Many people might be up in arms about putting Macdowell in my top 4. On another day he might not make it. This concerto is really quite brilliant. I don't know why more people (especially romantic era lovers) don't listen to Macdowell a lot. I for one am a fan of his sonatas.
4. Khachaturian Piano Concerto
Some call it overly-bombastic. I call it a jaw dropping experience. I absolutely love this concerto. It is original, it is Khachaturian. And you have to listen to it 5 times before you can really start enjoying it. But it is well worth the investment.