Wings
I'm in a particular Mozart mood again, so I'll go for Mozart's Piano Concerto No. 20 in D minor. The first movement is absolutely sublime. <3
Grieg's piano concerto is catchy and filled with energy--and the fact that it's been used numerous times in pop settings helps contribute to its popularity. I like it myself, but it can be rather cringe-worthy in crude pop settings or rendered ineffective by overly sappy performances.
Rachmaninov's 2nd and 3rd are also on my all-time favourite's list. Beethoven's are enjoyable...Mendelssohn's 1st, Liszt's 2nd, Brahms' 2nd, Schumann...hmm, and I've taken a liking to Ravel's Piano Concerto in G major lately.
I played Mozart's piano concerto in D minor (violinist). It's as fun to play as it is to listen, if not more so. Also, though not a concerto, Dvorak composes amazing piano quintets. There's one in A major, which is perfect for a rainy day and one in a minor that explodes my mind every time.