Greatest movies? Or favorite movies?
Greatest movies:
Godfather 1
Godfather 2 (too close to call, but #1 did it first

)
Seven Samurai (one of the most influential films ever)
Shawshank Redemption (a masterpiece IMO )
LOTR trilogy (best trilogy ever, and some of the best movies ever)
Star Wars
Empire Strikes Back (empire was better, but it wouldn't have existed without the other)
Raiders of the Lost Ark (best adventure movie ever, IMO)
The Good, the Bad, and the Ugly (if you haven't seen this, see the extended director's cut)
Bridge On The River Kwai (this movie is so good on so many levels, it's scary)
To Kill a Mockingbird (very, very good, especially for the era)
Not in that league, but still all-time:
The Right Stuff
The Usual Suspects
The Man Who Shot Liberty Valance
Fight Club
Apocolypse Now
Goodfellas
LA Confidential
The Sting
Tora! Tora! Tora! (very, very good. makes pearl harbor look like meaningless pap, which it is

)
The Sixth Sense (still remarkable even if you know what happens)
A Day at the Races (Marx brothers!)
Well, I've given enough for you non-classic people to chew on