Hitchcock, Mitcum, Bogart...all classics, but mostly not what I'd consider "off Hollywood" though certainly they are immortals. Love Hitchcock though - you mentioned Rope, which I think is one of his more innovative films - "Rear Window" and "North by Northwest" would be two other favorites, but that's big-time Hollywood IMO.
There's a whole other category that fits in that mold that few have mentioned: Documentaries! There are some truly wonderful documentaries that have been made entirely outside of the Hollywood machine. Top of my list would be:
Crumb
I Like Killing Flies (I mentioned that one already)
Grey Gardens
Mr. Death: The Rise and Fall of Fred A. Leuchter, Jr. (anything by Errol Morris for that matter)
Deliver us From Evil
Lake of Fire
Why We Fight
Who Killed the Electric Car
A couple of other films that popped to mind, albeit some of these are Hollywood efforts -
Being John Malkovich
Adaptation
American Beauty
10 Items or Less
Broken Flowers
Basquiat (brilliant performance by Jeffrey Wright)
What about films so bizarre that they are rendered tolerable only by the hard-core, and even then test the limits. I can think of one in particular, which I wonder if anyone else here as seen. Named by Time Magazine as one of the most important films of the 20th century:
Begotten - this film makes "Eraserhead" and "Tetsuo: The Iron Man" seem like Saturday morning children's cartoons.
A very strange and beautiful film that I CAN recomend, however: Jan Svankmejer's gorgeous animated film called
"Alice" (based upon Alice in Wonderland)