Depressing? Any of the ones written in the minor key. Most well know is The Pathetique Sonata in C minor. It is the 8th of Beethoven's numbered sonatas. Its original title was the Grande Sonate Pathetique and was dedicated to Prince Carl von Lichnowsky, a friend of Beethoven's
For a song to be good and depressing would be quite contradictory... I think you are referring to 'moody' or 'dark' or maybe 'melancholy'. As mentioned, look for songs in minor keys. For a very short list;
-Beethoven's 24th concerto, plus many of his sonatas
-Chopin's 2nd Sonata
-the first part of Lizst's 2nd hungarian rhapsody
-The Paganini concertos, especially 1 and 6 (not piano, but plenty 'depressing' as you will)
..there's literally 100's of thousands and to find what YOU like, just listen to various composers, i recommend classicalarchives, $20 for a year subscription
Rachmaninoff's piano concerto #2 in C minor is passionate, beautiful, and sad.
It makes me cry and also feel happy because parts of it feel like the world blooming and then the low, low keys playing and the orchestra in the background. Highly recommend that one.
Since you love Beethoven as I do, please check out Piano Concerto #5.