One of the most influencial films ever.

others you should check out are:

THe Searchers

L' Avventura (You must have patience with this one)

The Bicycle Thief

Lady From Shangai

The Big Heat

Casablanca

Psycho

Le Mepris (Contempt)

Rome Open City

Seven Samurias

Godfather

Weekend (another Godard film that I find funny but has a powerful message behind it)

Manhattan

Vertigo

Some Like it Hot

400 Blows

Uh that's all I can think of right now but I should be able to come up with more.