Super Street Fighter 2, SNES
Short but oh-so-sweet, the SSF2 intro may not seem like much to the masses raised on hour-long high-definition FMV cutscenes, but back in 1994 this was a sight that make me fair tremble with excitement. I think it's the giant, beautifully animated sprite that does it. It certainly makes it seem as though Ryu is really intent on kicking your ass, and the huge "SUPER" that follows left you in no doubt as to just how good the game was going to be.
Ninja Gaiden, NES
This was probably the first videogame I played that attempted to be cinematic in its cutscenes, and it just blew me away. Plus it starts with two ninjas with swords throwing themselves at eachother, so I was always going to be impressed. The way the music changes as Ryu starts telling his sad tale is expertly done, and the whole thing sets up Ninja Gaiden's plot quickly and impressively.
Mega Man 8, PS1
First off, this is the Japanese version, which is superior because it contains the "Electrical Communication" theme song instead of the fairly generic music that replaced it in the other releases. Secondly, it's like a little Mega Man cartoon! That's the sort of thing that makes me happy. Seeing a bunch of the old Robot Masters is nice, and it even includes Shade Man. I have to wonder about Pharaoh Man though, just standing there while Mega Man throws a train at him. I suppose it's not the kind of thing pharaohs are used to dealing with.
Neo Contra, PS2
Four minutes of glorious madness introduces you to Konami's not-actually-awful Contra reboot. You want missiles being chopped in half by sword? Gymnastics performed on artillery guns? Men riding atom bombs? Well, you got it. You also get some woman wailing "NEO CONNNNTRAAAA!" but you'll just have to excuse them for that. This is what all intro movies for action games should be like; balls-out, testosterone-fuelled insanity which ends in some slightly homoerotic hand-clasping. Brilliant.
Resident Evil, PS1
I really have saved the best for last here. This is my favourite video in any videogame ever, and it is at the same time both hilarious, terrifying and the coolest thing I have ever seen. No matter what Capcom do to Wesker's character, no matter what Matrix-esque powers they give him, to me he will always, always be that bored-looking guy at the end of this video. This intro raises a lot of questions, too, such as "Why does Jill shout "JOSEAHH!?"" and "Why do the dogs stop attacking them while our heroes stare at the departing helicopter?", but these are not questions that need answers. Indeed, to answer them would only sully the joy that is the Resident Evil intro. All in all, it is a truly glorious thing. But I doubt we will ever see its kind again, and that's sort of sad. Plus, it's better than all the live-action RE moves combined. These people can act better than Milla Jovovich, that's for sure.