Oh, God, you have opened Pandora's box here. At least for me.
I love "classical" music as many people call it and I really can't pick one or two favourites. Each day I would have to choose a different one.
Today it may be Haydn's cello concerto in D, for example.
Why do I love it? I don't know, I just do. It touches me. I can't say why, I just have some sort of special connection with Beethoven, Bach, Mozart, Chopin, Debussy, Prokofiev or Stranvinsky. And about which kinds... well, anything from the sixteenth century to the twentieth. I have some trouble with Schönberg, Stockhausen or John Cage, but I think the music from twentieth century has real jewels, though they're a bit harder to appreciate (for me).