I'm not really that into classical music, despite running that section in an HMV for a while some 17 years ago (I liked running Dance & Urban more; back then, we could order pretty much whatever we wanted, so the people of Essex had a huge range of Anticon and Big Dada to choose from) but when I find something I like, I really like it.
The Seoul Philharmonic Orchestra rendition of Tchaikovsky's 6th Symphony never fails to put a lump in my throat, especially when a single tear drops from the conductor's eye after the finale. You'd have to be made of stone to not feel something.
Then there is Rachmaninov's The Isle of the Dead, probably the most metal piece of music of all time. No metal band could make something this dark, though Godspeed You! Black Emperor get close with The Dead Flag Blues.