I agree with every word of Hypno-Toads’s post.
I chose The Shining, but it was close with 2001
I just now realized that not a single person has picked Eyes Wide Shut. C’mon, peeps! Where’s the love? 
OK, OK…Nicole’s tits are quite nice. But those are the only redeeming features of that pile of crap. Except maybe her ass. Sexist and shallow is the only way to appreciate in any way the absolute nadir of Kubrick’s career.
2001
A Clockwork Orange
The Shining
One of the benefits of Quentin Tarantino’s Hateful Eight was that the local theater that obtained a 70mm projector for it KEPT it and I got to see 2001 in 70mm this year.
I like that film much more than most people do. I’ve never understood the hate. Sure, it feels “cold,” but that’s the point. I thought it was a compelling story told well enough, and for me it brought up some important ideas (e.g., sex vs. love).
Not good enough to make the top 3 list, but nor did I rule it out when I first looked over the full list. I thought about it for a moment, but quickly noticed there were at least five films that were better.
2001, Strangelove, and Eyes Wide Shut are the ones I’ll continue watching if I stumble on them while channel surfing.
I really like Eyes Wide Shut (but then again, I like Waterworld) - the cinematography is like heroin for my eyes, the story’s dark and sexy, and Sydney Pollock’s acting is horrendous.
2001, Dr, Strangelove, and Full Metal Jacket, in that order.
I’ll go against the grain and mention that I absolutely love Barry Lyndon, but then I seem to be able to sit through many a movie that others frequently find tedious (like 2001, come to that).
OTOH, I’ve never been much of a fan of The Shining or A Clockwork Orange. Both have amazing visuals and great performances, but in the former case I just don’t care much for the horror genre, and I find the latter a bit too simplistic regarding plot.
I really love Barry Lyndon. It’s a long movie, and slow. But I was thinking about it recently, and I realized that I like it for a lot of the same reasons I like Breaking Bad. It’s very methodical, deliberate, gorgeously filmed, and each scene builds up more and more dramatic tension as this entitled outsider tries to worm himself into an insular group where he doesn’t really belong, only for it to be his own downfall.
I gotta dig out that DVD again.
Barry Lyndon all the way, it was hugely influential on the next generation of filmmakers such as Ridley Scott (watch his first film The Duellists and you’ll see what I mean.)