"You call down the thunder. I'll reap the whirlwind."

It's not my favorite, but is a game I recently played so...

Boyd: "I am the milkman, my milk is delicious."
Raz: "Boyd? Are you okay?"
Boyd: "Time for the final delivery to this address."
(Boyd picks up some milk bottles)
Raz: "Hey, is that milk regular kind or the exploding dream kind?"
Boyd: "It's fortified with what the world wants. What the world deserves."
Raz: "Are you sure that you don't want to just... talk about this Boyd?"

and also...

"Hey Boyd, why are you trying to burn down the asylum?"

I lol'd throughout most of the game, but the Asylum part was just... brilliant. The whole game is highly quotable...

From the Saint's Row 2 intro. Just popped this in today and found it to be funny.

TV Reporter asks, "As a student here, what are your thoughts on the drug problem facing this campus?"

Guy says, "Oh, I'm not a student here, I just come here for p*%$@."

Final Fantasy VIII:

Opening "I’ll be here… Why? I’ll be ‘waiting’ here… For what…? I’ll be waiting for you so… if you come here… you’ll find me… I promise." (inmortal words, it was one hell of an opening FMV)

Squall: No matter what happens, even if you become the world’s enemy,
I’ll be your knight.

Super Mario Bros 3:

Peach: Thank you Mario, but your princess is in another castle... ha ha ha just kidding

Mortal Kombat:

Dan Forden: Toasty!!!
Scorpion: Get over here (or come here)

Megaman X2:

Sigma: "I don't understand... why did Zero... he is... last of the doctor's creations..."

Contra (Japan):

Red Falcon: !"$%&/(*)¨)=??¿=[)({/!&%"%·/!Ç("·/·"!)@)! (Random characters, It's supposed to say something about they'll be back)

Super Mario 64:

Mario: It's a Me, Mario
Mario: Let's a Go

All of these http://www.imdb.com/title/tt0192565/quotes

G...A... M... E ... O .... WOO.... E..R
G.A.M.E.O.WOO.E.R
GAMEOVER
GAMEOVER
GAMEOVER

"DAYTONA USA"

There's lots, but some that come to mind:
'The universe is a yawning chasm filled with emptiness and the puerile meanderings of sentience' - Eternal Darkness
'Psychic powers...' - Resident Evil 4
'If challenge had a taste, you'd be quite delicious' - No More Heroes
'You're sick' - 'So are you' - NMH
'Eye of ze tiguhr' - NMH
'Wanna know the name?' - Devil May Cry 3
'This is my kinda rain' - DMC3
'I make it a point not to date women who shoot me in the head' -DMC3

• "Whose footprints are these?" Guard, Metal Gear Solid
  
• "Six bullets. More than enough to kill anything that moves." Revolver Ocelot, Metal Gear Solid
• "Do you want to save, Snake?" Mei Ling, Metal Gear Solid
• "Guten Tag!" Hans Grosse, Wolfenstein 3D
• "Who would be stupid enough to leave the base undefended?" Sima Yi, Dynasty Warriors 5: Empires (yeah, this is a cheap one)
• "Need a Medic!" German soldier, Wolfenstein: Enemy Territory
• "Sss!!!" Strogg soldier, Enemy Territory: QUAKE Wars
• "The humans will think twice before haxoring our leet tech." Strogg commander, Enemy Territory: QUAKE Wars

That's all I can remember now.