Snake?!? SNNNAAAAKKKKEEE!!!

"Some people just need killin'"
-Solid Snake

"I need a weapon"
-Master Chief

"..............."
-Link

A few of my favorites:

"My name is Tali!"

"Keelah.  What is it?"

"I love this place!  The crowds, the action--it's great!"

"Checking up on me, Shepard?  Don't worry, I'm still here--but after we stop Saren, I'm gone.  My pilgrimage can't wait forever."

Well they're memorable to me, dammit!

I am terribly shocked that perhaps the most famous game line of all time has not been mentioned even once in this thread.

"All your bases belong to us."

"You were almost a JILL SANDWICH."

"Blood. Hope this is not CHRIS'S blood."

"It's a weapon. It's really powerful against living things!"

-Resident Evil's own Barry Burton

Can't let you do that, Star Fox.
Andross has ordered us to take you down.
Peppy! Long time no see!
Andross' enemy is MY enemy.

haha this might be a lesser known one. My buddy bought mortal kombat shaolin monks for xbox, so we were playing through, and there's this cutscene where Baraka, the dude with like blades that come out his arms, picks up some bystander, plunges a blade into his chest 3 times, his head, and his stomache, and then throws him like 100 feet into the air. After he hits the ground, Liu Kang runs over and asks "are you ok?" Hahahah it was hilarious. You'd probably have to see it to understand it

"Thank you for clearing my back passage"