FINALLY, I SEARCHED THIS THREAD TO MAKE SURE SOMEONE PUT IN GLADIATOR. I looked at my Blu-ray collection to find some nominees: - Gladiator - Big Lebowski - Children of Men - Interview with a Vampire - Eternal Sunshine of the Spotless Mind - Empire Strikes Back Mind you, this is just from looking at my Blu-rays. I'm too lazy right now to make an actual list.
The Room is a cinematic wonder that needs to be experienced by all. You'll wonder what the director could have been possibly thinking, you'll wonder why any actor would sign on for it, but you'll also wonder why more theaters don't show it because it was absolutely one of the most fun theater experiences I've ever had.
I liked some of the others you listed, but I despised Andrei Rublev. That film can swallow a couple gallons of molten steel for all I care. I did want to watch any of this film again, and the slaughter of a live horse really pissed me off. Stalker and Solyaris were Tarkovsky films that were much more to my liking.