Not from the Classical era but under the general category, I love Charles Ives. He may come across as a difficult and overly experimental composer, but his music is often playful or full of mystery and deep emotion. Even his stranger more dischordant work doesn't really come across as crazy to my ears, and it lacks the anxiety that Rev. Powell mentioned about many early 20th century atonal works.
Here's one of his quarter-tone pieces:
The lovely 3rd movement from his fourth symphony:
A recording of Ives himself playing The Alcotts
from his Concord Sonata
I think most of the stuff I own on CD is from the 20th Century, stuff like Mahler and Shostakovich. For some reason I have like, 3 recordings of Rautavaara's Angel of Light
. I'm ashamed to not even own any Mozart of Beethoven!
I have difficulty getting into opera. I only own one actual opera recording and it's of Messiaen's St. Francois d'Assise
. I've had it for a number of years but have only listened to the 1st of the 4 discs in the set.