Schubert - Piano Sonata in A Major, especially the second movement is one of my favourite pieces of music. It's tragic he died so young. I think he knew he was dying when he wrote this - it sounds like it anyway!
I love more minimalist composers like Satie and Arvo Part too. The Gymnopedies are all amazing but I think everyone overlooks Satie's nocturnes. I also think he's pretty unfairly judged as a not-so serious composer due to his eccentricity and slight compositions. The 2nd and 4th of his nocturnes are my favourites.
Arvo Part's Spiegel im Spiegel is probably the most calming thing i've ever heard. Love it with the cello.
and speaking of cello, i've recently started listening to Leos Janacek's suite for strings and this part is amazing: http://www.youtube.com/watch?v=xx1PBU3BuK8
and Debussy's nocturne! http://www.youtube.com/watch?v=uyZJ3rNb4xM
i've only recently started listening to classical music in the last year or so so i'm still trying to wrap my head around it but I can see it becoming an obsession tbh.