Best movie (not favourite) for me is probably 2001 : A Space Odyssey. It is rare in that it really is a 'pure' movie in that the visual images and clues are the real meat of the film. The script is just an element and the actual dialogue deliberately banal.
As such, given all its other qualities, I'd say its the best film as most great films tend to rely too much on dialogue/narrative design borrowed from books, another far older medium, whereas Kubrick set out to leverage the film medium primarily.
Favourite is too hard to call, but the following, many of which have a claim to being 'best' too, are a good list:
Blade Runner
Lawrence of Arabia
Alien
The Godfather
Bridge on the River Kwai
When Harry met Sally
The Terminator
Aliens
Mean Streets
Goodfellas
The Matrix
Blood Simple
The Empire Strikes Back
The Fellowship of the Ring (my favourite book/film of the sequence)
Solaris
The Incredibles
The Iron Giant
Near Dark
Mad Max 2
Recent films I've enjoyed but not sure how they'll stay with me:
Moon
Up
The Hurt Locker
Try to be reasonable... its easier than you think...