I have a few contenders, depending on category of film...
Fight Club. I saw it in the cinema having heared or seen nothing about it, not even the novel it is based on. It blew me away. The same for the original Matrix - no prior knowledge and it was great. The sequels sucked though.
Saving Private Ryan. Yes, it has Tom Hanks in it, but it has the credit of being the only movie that has reduced me to tears so far. I fel it conveys the horrors of war and the waste of life in a personal and tragic way. District 9 made me feel similar about how we have a capacity for evil that comes to the surface too easily.
Full Metal Jacket. Simply for its first half, with the whole dehumanisation process. Brutal. Hambrger Hill also deserves a mention here, as does Glory.
Twin Town. Massive bias here, as it was filmed where I grew up with local actors and many scenes filmed with "unaware" extras". A tale of growing up in a deprived urban area, and of revenge. Some fantastic black humour. I enjoyed Fear and Loathing a lot for its similar twisted humour.
Life of Brian or Quest for the Holy Grail by Python are probably the funniest.
Alien. Simply shit your pants scary by using tension and clever cinematography, instead of overuse of the monster. Blade RUnner shares some of the same style that I enjoy.
I am sure I have missed some that will come to mind once I think a little more.
Edit: Oh, yes... Das Boot (oh man is it tense) and Being John Malkovich (its just the right amount of crazy, especially when Malkovich gets insde his own head).