Manny Calavera: Take Five - Dave Brubeck
Niko Bellic: I Still Haven't Found What I'm Looking For - U2/Immigrants Song - Led Zeppelin
Master Chief: Bridge Over Troubled Water - Simon & Garfunkel
Razputin: My Body is a Cage - Arcade Fire
GLaDOS: Everything In Its Right Place - Radiohead
Kratos: Reckoner - Radiohead
Mario: No Sex For Ben - The Rapture

OK, I thought of even more, because I like thinking them up:

San Andreas: Banned in DC by Bad Brains
/* Ok, it's not a game character but I like it anyway */

Logan Keller from Rainbow Six Vegas: Viva Las Vegas by Elvis

Main Character from Crysis: Holiday in Cambodia by the Dead Kennedeys

Kratos from God of War: Angel of Death by Slayer.

Gordon Freeman-Muse: Knights of Cydonia

In fact, the whole of Black Holes and Revelations could have been used as a soundtrack to HL2

Link's song would have to be "Once Every Lifetime" by Jem

Yorda - Greenfinch and Linnet Bird from Sweeney Todd.

I hope I'm the first one to suggest something from a musical.

HK-47: This Machine by Julien-K
Sam Fisher: Secret Agent Man by(who the bloody hell knows?)or I can't Decide by Scissor Sisters
Just about every main character from GTA: My Generation by Limp Bizkit
Jedi Exile from KOTOR II: Rise up by Drowing Pool or I can't Decide by Scissor Sisters
Turok (Is that his name?): Welcome to the Jungle by Guns n Roses

And I agree with Balding Steve. Link's got no social skills, so the sorry excuse for an existing being has...

NO CHANCE IN HELL

Creepin' and a Crawlin'- The Zutons for the protagonist from Bioshock
Supertheory of Supereverything- Gogol Bordello for Gordon Feeman

Travis Touchdown - No More Heroes (No Shit)

Violence Fetish by Disturbed - Leland VanHorn from Condemned.

Alright, I thought of a few more. For Pyramid Head, Scream by Avenged Sevenfold. Solid Snake, Bombshell by Powerman5000. Sam Fisher, The Name of the Game by The Crystal Method (the song to the opening credits in the first game). Every protagonist in GTA history, Gangster Gangster by Lil' Scrappy featuring Lil' Jon. That's about it for now.

Doomguy - "Walk With Me in Hell" by Lamb of God

defcon 1:
Neutron Bomber by WASP for TF2's Pyro or MGS3's "The Fury"

No! Firestarter by The Prodigy :~D Much more suited...