I like the trailors for Assassin’s Creed… not played the game so dunno if the intros are the same, but the trailor is kinda cool.
my fave is the intro to Wipeout 3 for Playstation. The first half is interesting, but the second half, with the animated logos of each team, is so great. The logos are incredible, and the animations themselves have so much character… I could watch it for hours.
The Designer’s Republic (which designed the logos/anims) rocks. 
Yet another one in the same universe - MechCommander 1 Intro.
The intro to Tourist Trophy gets my blood going pretty good.
Oh yeah. I also like that one…er, Mech arrior Vengeance I think? It’s where all the mechs are killed exiting the hangar bay but one. It’s his speech really.
He tries several times to raise the palace, his own defense; no one answers. It’s the speech that says in the middle…
“Any receiving unit. (snip) I’ll hold them off as long as possible.”
And he proceeds to do so, alone, against three mechs. He is taken down quickly, but I love the scene.
Master of Orion 2 was badass.
Shadow of the Colossus rocked too.
FF8 and 10 both had outstanding opening scenes.
This the one? Couldn’t agree more.
Well, I can’t see it at work, but I think it’s the one. I’ll let you know from home.
R.I.P. Looking Glass Studios. Here’s hoping Bioshock lives up to the legacy.
At this point, I can’t see how it couldn’t. As awesome as all of these intros are (and they are awesome), the initial Bioshock trailer blows them out of the water.
And yes, the game really does look that good.
Mechwarrior 3 has a pretty snazzy intro too. I just love the pilot of the Atlas mech, the master of understatement.
And is it just me, or does the MadCat exist to be the Kenny of the Mechwarrior intros?
I rather liked the intro to Wing Commander IV, the greatest movie ever made for the PC. It’s a LONG intro though, Youtube should have links to parts 2 and so on.
Another vote for Final Fantasy VIII, though with a complaint: The intro makes NO DAMN SENSE. That said, awesome music and a kickass swordfight.
Oh, and a “Me Too” for the System Shock 2 intro.
“I command you…to RISE from your grave and rescue my daughter!”
I thought of mentioning this one, only because it’s one of my favorite games of all times. The cinematic wasn’t bad looking, problem was it didn’t capture the feel of the game at all, much less convey any background details about the story, the different races, or the history of the Antarans and why’d they’d be attacking a space station. Guess they left that info to the manual and couldn’t be bothered with it in the game? There’s no focus in the game on even having fighters scramble from a space station. The voice acting was totally sterile and the dialog towards the end didn’t even sync up with the action … the dude saying “launch emergency distress beacon NOW” is doing so as the station is already exploding. There have actually been quite a few intros which have contributed nothing to the game they’re attached to, and sadly this is one of them. The ending cinematic was rather pathetic too, and was the same no matter what race you were. It’s like they outsourced the cinematics to some group that didn’t have any idea what the game was about and rushed them out the door in a week. Then again, the MOO1 intro wasn’t much different. Such a shame, because both games are absolute classics.
I also like the MW3 cinematic. The game is my favorite of the series, anyway. MW4 had a great intro, but did anyone else feel the gameplay was a departure from the previous titles because the units were so nimble? It just lost the feel of piloting a giant lumbering war-machine in favor of a faster pace of action. I did like the addition of legs getting damaged and causing a limp though, instead of just getting completely blown off like in the previous games.
Moving on! Eh, how about … the intro to The Adventures of Willy Beamish?
Final Fantasy IV. Sort of. It’s a simplified version, with some story elements changed, and several abilities removed altogether. It’s been rereleased under the original title with most or all of those parts restored (as well as bug fixes) for Playstation and Gameboy Advance (which also has tweaked graphics and added content).
Anyway, my candidates.
We 
Katamari - the graphics style, the narration, the story and its wackiness… All classic.
Final Fantasy’s isn’t an introduction so much, as it comes in after you’ve played the first portion of the game, but when it shows the title and backstory, as simple and primitive as it is, it really works.
Anyone else remember “Skeletons In My Closet,” the jazzy closing music to the game?
Some great ones are already mentioned but I have to give the original classic intro to Trinity.
For those not familiar with the game it was an Infocom text adventure where you play about a dozen moves of the game before the plot hook and adventure title appear. It’s kind of a precursor to the “play through” intros that were popularized by Half-Life.
I’d also like to nominate Red Alert 2, which has enough cheese to kill a lactose intolerant person simply from looking at it.
“I don’t give a wooden nickel about your legacy!”
For newer games, Halo 2 certainly deserves a place, though only if you include up until the beginning of the Covenant attack on the MAC platforms (which isn’t included in the Youtube clip I found.)
The intro for Black & White was excellent. Pity the game wasn’t as good. 
And System Shock is one of my all-time faves.
The Warcraft II movies are all fantastic, really, but this particular outro is my favourite: http://www.youtube.com/watch?v=MgJK4WpOImM&mode=related&search=
(Tip: Catch the guy being tackled around the 40 second mark)