I will second Vertigo from Jetson's list, Jimmy Stewart was never so creepy and I feel its Hitchcock's strongest film. Best soundtrack of his films as well in my opinion.
The Third Man is also a great flick. It is black and white but its a beautiful film for black and white. Shot in postwar Vienna the photographers did a great job of capturing the city and making it a solid part of the tale.
Some films I did not see on anyone's list but highly recommend:
Lone Star by John Sayles is another must watch. It's probably John Sayles' magnum opus in both screenwriting and directing. Lone Star like many of John Sayles' films is a tale about a community told through the lives of individual characters in that community. Wrapped up in this exquisite narrative is a murder mystery, a tale of unrequited and forbidden love, the search for identity as a people and as an individual, and ultimately a man's conflict with his father. All of it is brought together beautifully in a very powerful statement in the film's conclusion. Yes all of that is vague, but trust me the film is brilliant.
Another one is a recent film that I think may be the best film of the 21st century so far.
The Last King of Scotland directed by Kevin MacDonald is about a young Scottish doctor who runs off to Africa to get away from his parents and for other idealistic reasons. He becomes involved with Uganda's strongman ruler Idi Amin by treating his hand in the village, and is soon ensnared into his organization by the force of his personality. Idi Amin is played by Forest Whitaker who was absolutely deserving of the Oscar he earned for this role. Its a tale of tyranny and mistrust of the vein of another classic Scottish Play, Macbeth. Idi becomes increasingly violent, paranoid, and controlling as the yoke around his rule tightens. I highly recommend this film.
The Battle of Algiers is a film by Gillo Pontecorvo about the violent civil war in Algiers that pitted its French colonizers against the general arabic and islamic natives. Set in the city of Algiers the film follows several different narratives including the viewpoints of terror cell leaders, french security officers, and the French Colonel that comes in to establish martial law. The film is forty years old, but has stunning commonalities with Today's struggles with Terrorism. Cent Com actually screened this film as a discussion starter for dealing with Terrorism after 9/11. It has a lot to say on the matter without being a dry documentary.
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What am I supposed to have seen?