Well, okay, not the best cinematics ever -- just some of my favorites. I'm sure I'm missing tons of great ones. But this is the kind of thing you post on a Friday, right?
Chronologically (These are spoiler-heavy, so beware):
Ninja Gaiden (NES, 1989)
This is the first memory I have of the honest-to-goodness cinematic opening to a game. I love everything about it: the close-ups, the extreme widescreen, and especially the music. This kind of thing wasn't common when Ninja Gaiden came out. It was mind-blowing.
MechWarrior 2 (PC, 1995)
This played right as you booted up MechWarrior 2. I liked the game all right, but I must have watched this sequence -- estimating conservatively -- a hundred million times.
Resident Evil (PlayStation, 1996)
OH SHIT IT'S A ZOMBIE
Final Fantasy VII (PlayStation, 1997)
This is the most famous sequence in the game, although another great choice would have been Sephiroth vanishing into the flames of Nibelheim. I knew this moment was coming when I finally played Final Fantasy VII in 2003, but it was no less powerful for that. It's so strange to watch this now: I remember seeing commercials for this game and thinking that the FMV looked real.
Metal Gear Solid (PlayStation, 1998)
Metal Gear Solid is essentially one long cutscene punctuated with bursts of gameplay, but when they're done this well, who cares? Each foe Snake vanquishes gets a big, dramatic death scene, but Sniper Wolf's was always my favorite. I think I like the contrast between Snake's reaction and Otacon's. "I don't have any more tears to shed" is such a good line.
Shadow of the Colossus (PlayStation 2, 2005)
Watching this now, the moment doesn't seem so dramatic, but at the time I actually yelled, "No!" Shadow of the Colossus does such a wonderful job creating an atmosphere of loneliness and desolation. Agro is your only companion -- almost the only sign of life in the whole world -- for 90% of the game. And then this happens, like a punch in the stomach.
The Darkness (PlayStation 3 and Xbox 360, 2007)
This may not technically count as a cinematic, because it happens in-game, but considering that you don't control your character I think it passes the test. This is just one of the bleakest and most horrifying scenes I've ever encountered in a game, completely unleavened by irony or comic relief. Its impact is heightened by the scene earlier where you and Jenny sit on the couch together watching To Kill a Mockingbird. I wanted to kill the hell out of Uncle Paulie after this.
Post links to your favorite cinematics in the comments!