I know I'm kinda bumping the thread, but I felt like a prize idiot when I realised I had left this off my list:

Wizardry 8 - Kind of simple, but just felt right for the series.

I LOVE Fallout's intro. I also loved the Fallout 3 opening scenes/Vault life. Haven't seen 2's yet.

Not the best intro ever made, but Master of Magic made an impact on me for some reason.
No idea why, but the "Old man" bit always stayed with me.

The Lands of Lore intro stayed with me because of Patrick Stewart.

My favorite intro is probably a toss-up between , [url=http://www.youtube.com/watch?v=5ITiEm6W5EM]System Shock and Fallout.

Man there are a lot of good intro's.

This might not be an intro or an opening scene but still remains one of the most awesome scripted moments in a history of espionage :)

http://www.youtube.com/watch?v=SKDgXJ22Rmw

Chrono Cross
Final Fantasy VIII
the openings are great

Not my favourite, but since no-one has mentioned it yet; Need For Speed 2 SE
http://www.youtube.com/watch?v=6OwZNx7bsMo

I'm not really a big fan of racing games, but NFS was a great exception.

Oh, and let's not forget the most epic intro of all gaming: Day of the Tentacle!
http://www.youtube.com/watch?v=2BRXmgcBHBM

God of War 3
Darksiders
Magic & Mayhem