For the Greatest catagory I'd say:
The Shawshank Redemption
or
Green Mile
I never saw Saving Private Ryan, But I want to as I heard that it is a GREAT movie.
For a favorite movie, to me, it means that the movie has to be worthwhile enough to buy and watch again and again.
for me those would be:
Drop Dead Gorgeous [a much underated comedy. Maybe only funny if you live in the midwest USA. Plus, it's so 'Politically Incorrect' and pokes fun at everything taboo in today's society.]
Die Hard #1 [saw it was TV the other week and it's still good. Has some of the best lines and villians ever put on screen]
Road Warrior [one of the best chase scenes ever!]