[Sethomas]

I hate hate HATE that self-perceived counter-cultural prententicons worship it for its place in A Clockwork Orange, but a good performance of Beethoven's choral rendition of "An Die Freud" (the final movement of what I think is his Ninth Symphony) is a life-affirming experience in audio form. Hence, it's also just about the most popular melody in existence (although Beethoven's Fifth was purported to be the most easily-recognized) and is the anthem of the EU.

Other classics on my playlist are Mozart's Requiem (you really can't over-state its necessity), The Great Gate of Kiev, Rhapsody in Blue by Gershwin (not really classical, but it belongs here), and playing LOOM all those years in my youth made me really love Tchaikovsky's Swan Lake.