I've always found Pärt too sacred & celestial for my taste, but perhaps I've heard the wrong (=most famous & popular ie easy-listened) pieces?
Franz Schubert managed composing some really sombre & brooding Lieder, like "Doppelgänger" -
http://www.youtube.com/watch?v=fKVnL9JvuO8 (the Pestdemon tape Doppelgänger is of course more than slightly inspired by this piece).
Chopin's prelude in C minor, which you all know from a certain Italian movie:
http://www.youtube.com/watch?v=c97LsxyoZW0&feature=related (played by some guy, not recording)
Surprised no-one's mentioned Alfred Schnittke & his Requiem. His drifting in and out between minor and major tonality really messes with your ears, very dubious...
http://www.youtube.com/watch?v=GqdB3WU_CXIhttp://www.youtube.com/watch?v=75Dqh5PWbWo - Credo, with a nice drum beat. The deeply religious do it best.
Shostakovich, only getting bleaker and bleaker as the years progressed in Soviet until the '70s. This one is pretty classic, but still very doomy, far from uplifting..!
http://www.youtube.com/watch?v=gSoKpCXWF0Q&feature=relatedSome of his symphonies are rather heavy as well, I think no.7 ("Leningrad Symphony"), second or third movement, very war-like with this menacing snare ostinato...
Concerning terminology... no I think classical music would generally refer to pre-modern (Baroque through Classic period to Romantic period) art music, and I suppose most canonized Modernist art music... But I suppose classical music in it self reached it's peak and dissolved with Schönberg & the dissolution of tonality. And, of course, classic = canonized (by prominent German musicologists before the wars). It's hard to canonize already composers born in the 20th century. Or composers in pre-Baroque periods who worked under completely different circumstances than the supposed geniuses like Beethoven, Wagner etc.