In no particular order, my top ten:
Dr. Strangelove
Spartacus
Yojimbo
Lawrence of Arabia
To Kill a Mockingbird
La Jetee
Jules and Jim
The Good the Bad and the Ugly
West Side Story
One, Two, Three
The 60s are an interesting time for movies. There are the Hollywood blockbusters and the small foreign auteurs. American movies start moving toward the changes that happened in the 70s.
A lot of movies might be on my top ten on a different day.
I should probably include The man who shot Liberty Valence.
I chose the Good the Bad and the Ugly as my representative Spaghetti Western, but others could be in its place.
I chose West Side Story as the big Hollywood musical, largely because I think the opening is amazing and the Bernstein score and Robbins choreography are on a different level than most other musicals. But in that category it's hard to leave off My Fair Lady, Sound of Music, Music Man, etc.
I think the Graduate is overrated. 2001 probably belongs on the list, despite being overrated. I also think Strangelove and Spartacus are better and 3 for Kubrick would be a bit much.
Then there are some not so great movies that are guilty pleasures:
What's up Tiger Lily?
The Dirty Dozen
Barbarella (OK, just for the opening credits)
I also have to admit that I haven't seen a lot of 60s classics that are on most other people's lists.
[This message has been edited by biobioprof (edited 9/4/2010 2:35p).]