Meh... meh... meh... meh...

NOTHING beats Warcraft 3 Reign of Chaos! Nothing!

http://www.youtube.com/watch?v=jlOPBYIo6Kc

EDIT: Actually, scratch that... Nothing beats ANY of Blizzard's cinematics. :p

Not available in the US apparently lol

I like UFO: Enemy Unknown's intro because it almost perfectly misrepresents the actual game's tone.

Stonekeep
for sure
http://www.youtube.com/watch?v=TYfBq5XfC3k

One word: Moonstone!

I´ve always loved this, it feels just like the game:
http://www.youtube.com/watch?v=8N5ODEGR1KQ

That IS an absolute classic :-)

Legacy of Kain: Soul Reaver
http://www.youtube.com/watch?v=H7eOTHIV8y4&feature=related
or
Contra: shattered soldier
http://www.youtube.com/watch?v=Viki52UJFjE
Well, contra's intro is nothing epic but I liked the game back in the day. =)
5 or 7 levels and all hard as hell.

Lol, I actually like this intro though.

And yes i do own the game :3

http://www.youtube.com/watch?v=YlUwaarTZXc

I'll throw in a mention of Paraworld.

Most epic intro ever:
http://www.youtube.com/watch?v=HhIIyxNn_04

Runner up:
http://www.youtube.com/watch?v=1j4gO9sR7zs

If you can count it as such, the train sequence to kick off Half Life 1.

Doesn't quite explain anything at all, but even on the first play through, you know something is going to happen...

Ultima 9 intro

/thread

As much as people dislike that game, the intro scene is the best I have yet to see in a game for atmosphere and art direction.