Read the question - ooh tricky one. I don't actually have a no. 1 favourite intro.
For some reason, the first game that I immediately thought of was
Zelda: Twilight Princess (NGC/WII). I don't know why. It was decent but too short and not as good as the N64 Zelda intros.
Upon further reflection, here are a few of the intros I like.
Zelda: Ocarina of Time (An instant classic - like the game itself really)
Chrono Cross (PSX) Chrono Trigger (SNES) Snatcher (SCD) (catchy BGM - One Night in Neo Kobe City)
Grandia III (PS2) (I haven't started playing the game yet but I watch the intro from time to time. It's corny & cliched but I find it strangely compelling).
The two PS2 Tales released outside of Japan -
Tales of Legendia (PS2) &
Tales of the Abyss (PS2) ==========================================================================================
pezhead53: ...the DK Rap from Donkey Kong 64...
Ha ha. I remember that. "His coconut gun can fire in spurts. If he shoots ya, it's gonna hurt!"
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Tiko201: Snatcher:
http://www.youtube.com/watch?v=ZuyUShtcn94 Cyberpunk atmosphere and heavy synth music. What's not to love?
Exactly! Nice choice of intro.
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Elmofongo: ... To bad the game itself is incomprehensible :P
FFVIII.... Incredible intro, disappointing game. :P