I hate folks giving more than one answer to a question, but I can’t choose between Ivanhoe and The Big Sleep.What is (are) yours?
Dammit, I’ve got to get a Bogart hat like that…
2001 hands down. I just watched it again on my new 46" LCD TV - awesome. And I saw it in Cinerama when it first came out.
Duck Soup is probably second.
To Kill A Mockingbird and Body Heat.
Both if them move me…but that’s just me.
Casablanca
Natural Born Killers
I Heart Huckabees.
It’s a comedy about existentialism. I basically feel like this movie is tailor-made to suit my exact specifications. It is both hysterical, weird and thought-provoking.
If I determine “favorite” by “most likely to want to watch again and again forever if forced to choose one movie” then it’s The Princess Bride.
Trainspotting, still the one I will always turn to if it is on tv. I never, ever get bored of the dialogue and the scene in the bar, after the heist, between Begbie and Renton is a masterpiece.
OK, since we can do two movies; I would say one would be a tie between Eternal Sunshine of the Spotless Mind and** Punch-Drunk Love**. The second would be a tie between The Truman Show and Adaptation.
(I’m a Charlie Kaufman fan. Though I’m not fond of much of Carrey and Sandler’s comedic works, [especially Sandler’s], to me they’re pretty well suited for these roles.)
The Right Stuff
I’ll second 2001: A Space Odyssey. Soon as I get a big HD TV and a Blu-Ray player, it’ll be the first Blu-Ray disk I buy.
Casablanca.
But close behind it are The Fellowship of the Ring, Breaker Morant, Memento, The Incredibles, True Lies, Glory, Trading Places, Pride & Prejudice (2005) and Star Wars. 
I’ve never understood the slavish devotion of so many critics to Citizen Kane. Yes, it was innovative; yes, it’s a timeless story; yes, a young Orson Welles pulled off an amazing feat. But as a movie, it’s just not all that, IMHO.
**Rushmore **and Annie Hall.
The Royal Tennenbaums - I think this movie is so good that it almost hurts.
My runners up are:
Ghost World
O Brother Where Art Thou?
It’s a magical experience. It’s not my favorite movie, but 2001 is up there, for sure. It needs to be seen on Blu Ray. The only thing better would be IMAX.
My favorite is Fargo. I’ve probably seen it 100 times. I’m in love with Marge Gunderson. The relationship between her and Norm “son of a” Gunderson is terrific.
Unforgiven
The Godfather I and II; Rushmore; The Big Lebowski
Terry Gilliam’s Brazil.
It’s a dead heat between The Postman Always Rings Twice (the Lana Turner and John Garfield version) and Out Of The Past.
Oh man I hate answering these questions (although I love asking them). I always know EXACTLY what my favorite movie is, until the question is actually asked. Them, of course, it conveniently slips out of my mind never to be remembered again. So here’s my answer, although, I’m almost sure it wont actually be my favorite movie.
The Maltese Falcon and **Casablanca **my favorites but I’m usually not in the mood to watch those type of movies. I usually prefer either a kick ass action film or a really good comedy. As far as action goes, any movie with a good looking lady and some guns or martial arts will fit the bill but let’s just say my favorite is Kill Bill. In the comedy department it could be My Man Godfrey for the older stuff and The Big Lebowski for the newer films.
So to sum it all up, Bio-Dome with Polly Shore.