Look, I'm not sure how I would die were these movies to mysteriously disappear, but here's my list...totally random, and I'm certainly that I've missed a ton..and I'm not saying all of them are classics, either! And they're probably more "movies I really really liked," than anything...
1) Twin Peaks: Fire Walk With Me
2) Austin Powers: The Spy Who Shagged Me
3) The Band Wagon
4) Blazing Saddles
6) Star Wars (I'll pick the first one)
7) All That Jazz
8) Bringing Up Baby
9) Wizard of Oz
12) Y Tu Mama Tambien
13) My Favorite Year
15) Topsy Turvy
And some movies I never ever want to see again?
1) the DVD of Jekyll and Hyde with David Hasselhoff (gag!)
2) Breakfast Club
3) probably Pink Flamingos (once was enough!)