The intro to NHL 99 is one I like to remember. Part of it had to do with when I played it, but it’s pretty original too. The intros to the EA Sports games with fans or players saying “It’s in the game.” was cool when it started, not quite the same effect now, but still decent.
Me tooooooo. Damn, that is awesome. I especially love how it feels spoilery, but once you’ve played the game, you realize nothing in it actually meant anything without the proper context.
The intro to almost all Blizzard games past 1995 have been memorable.
Another vote for pretty much every Final Fantasy game.
The opening game-engine cutscene at the very beginning of the Dam level in Goldeneye absolutely blew me away as a kid simply because I had never seen anything even remotely approaching that level of graphics in an FPS up until that point.
Ditto for the opening of Final Fantasy VII - the shot of Midgar’s streets and Aeris walking with the flowers - the juxtaposition of weird old-style cars with the slick neon signs of the city threw me for a loop even as a kid and I never knew about the concept of cyberpunk, steampunk or any of the other variations.
The intro to Planescape: Torment is pretty fucking cool.
But I agree that the Dawn of War intro pips it to the post.
Battletoads, for the NES.
Surprisingly cinematic for a fistful of pixels.
“War…war never changes…”
The Bioshock into is quite good.
I just wanted to call this one out again. I remember playing it for the first time, and thinking, “Holy cow! I’ve played the game for about 15-20 minutes, and I’m just now getting the intro?! Cool!”
And the music matches the intro scene perfectly. It was with that intro that I really started appreciating the works of Nobuo Uematsu.
Final Fantasy VI intro - I think I watched it about a half a dozen times on the night when I first got it. VI wound up being my favorite of the entire series.
Starfox…taking a cue from Star Wars.
I’m sorry, I just don’t get it. It’s 3 robots walking up a hill. Music is decent. That’s it. 
What you’re seeing is a few minutes into the larger intro of the game. Before this there’s a bit of a setup telling you a tiny bit about who the three people are in the suits. Two are soldiers and the third is a magician whom the soldiers are mind-controlling.
Also, what you may not be able to see is the background with the city they’re going to attack coming up over the horizon. It is definitely unimpressive now but for SNES era graphics, this was hot stuff.
On top of all that, I live in Alabama and think snow is kind of cool. 
Two soldiers are mind-controlling a magician? You’re just making this shit up!
No I can appreciate that the graphics are great for the SNES. I guess I just never “got” those Final Fantasy games.
+1. It can be seen here. I personally think that intro set the standard of cinematic game intros in the years that followed. It is very brief, but I can’t remember an intro more intense intro than that prior to 1995.
Also +1. The ending to this game on the 3DO is probably my favorite ending cinematic of all time. And mind you, it’s over 15 years old! It’s nothing short of criminal that this cliffhanger ending still hasn’t been followed up with a proper sequel after all these years …
Well, the army devised special crowns that mentally subdue the wearer. The soldiers weren’t directly mind-controlling her. Does that make more sense?
Perhaps this will be more to your liking. It’s the opening of the FFVI remake for the PS1. FFVI always blows me away.