Le fabuleux destin d'Amélie Poulain (or just Amelie) (2001)
The very definition of joie de vivre. Jean-Pierre Jeunet's style is kinetic, the camera whipping about to follow any subjective whim of the central character (or whoever happens to narrating that particular bit). It's tone is whimsical, romantic, often grotesque, taking place in a magical 'Paris' of the imagination rather than a real city. Some found the mix too rich and sweet, like a cake with too much icing. I wasn't one of them.
Lord of the Rings Trilogy (2001, 2002, 2003)
Might as well consider them as a whole since their qualities are common to all three. Peter Jackson took the subject up like a personal crusade to convince the rest of us that Tolkein's world was not just for hippies, and he did it straight, without a hint of irony. Could have been kitsch in the extreme (and it sails close to the edge at times), but is delivered with such bravado and conviction, I couldn't help but be swept up in its epic wake.
Borat: Cultural Learnings of America for Make Benefit Glorious Nation of Kazakhstan (2006)
Sure, it was uneven and I sensed a lack of certainty about the tone, but that's because Sacha Baron Cohen and Larry Charles were blazing a trail, which doesn't happen too often, especially in comedy. Basically a mix of prepared sketches and seat-of-the-pants situational improvisation around a connecting theme, one is constantly astonished at Cohen's preparedness to put himself in danger (literally and comedically) and "go where no man has gone before".
Michael Clayton (2007)
Its finale should be taught in screenwriting 101: 'The Forgotten Art of the Perfect Ending'. Written by Tony Gilroy, the screenwriter of the Bourne films. A political thriller that just about restores one's faith.
Grizzly Man (2005)
The other great documentarian of the last few decades (see Errol Morris, below) is Werner Herzog, whose fact-based films are as important as his features and whose themes are a direct continuation of his particular obsessions. This displays many of them: nature as an implacable, and often malevolent, force; a visionary central character bordering on madness. Unforgettable.
Gosford Park (2001)
Robert Altman goes at the country house murder mystery with his typical dry and ironic disregard for the conventional trappings of genre. Instead of the hollow figures which usually inhabit these kind of things (Colonel Mustard in the hall with the candlestick), he furnishes the film with insightful, wry and funny observations about character and class. Various esteemed character actors have the time of their lives.
The Fog of War: Eleven Lessons from the Life of Robert S. McNamara (2003)
Errol Morris's signature interview technique of placing his camera so that the subject speaks directly into it has an almost painful intensity and gives the traditional 'talking head' a confessional quality. This has been demonstrated nowhere better than this film about the life and career of Robert McNamara, the highly controversial former U.S. Secretary of Defense. We witness a man attempting to make sense of the moral ethical choices he made, choices which may have lead directly to deaths of thousands, and come to appreciate the chiasm between intention and consequence. A film whose philosophical consequences are immense.
The Lives of Others (2006)
Successfully gives the uninitiated a taste of life as it was lived by innumerable millions under Communist rule across Europe until about 1990. Sure it's wish-fulfilment, and someone like the Stasi agent either couldn't have existed in the first place or wouldn't have survived long enough to perform the transformation depicted here, but it sure looks and feels like a genuine slice of the DDR, a 20th century panopticon.
The Others (2001)
An old fashioned horror movie, in the very best sense. So effective and skillfully told that it earns comparison to the best of the 1940s and 1950s. Nicole Kidman's nervy brittleness as an actor has never been better utilised. Underrated.
Almost Famous (2000)
It's neither as sharp or as funny as it probably should be, but has a grace and warmth that is memorable. Manages to feel perfectly credible without a line of coke or defiled groupie in sight. Owes a big debt to Billy Wilder, particularly 'The Apartment'.
Other 'Best films of the 00s' posts here and here.