After about 10 years, my husband still walks around the house humming/singing the "Mr. Death" song from The 11th Hour.
As for soundbites: the guy in the Nashkel Mines in BG1 who wanders around saying "Get me out of this h---hole!" in a singsong voice.
More recently, the goblin who ends up as a janitor in Neverwinter Nights and is always asking "Is it breaktime? Yes? Yes?! *pause* No, back to work..."
What other game soundtracks or soundbites do people remember even now?

Umm, for the brilliantly comic voice acting:
"boo hoo hoo, why me? snivel...."
the hostages from the Tac Ops mod for UT
and Virgil from acranums:
"thats the way to show those basta... I mean ummm, good hit sir!"

E1M1, and many of the other more memorable tracks
The Skitchin' soundtrack; Smog Dog especially
Everything from Toe Jam and Earl

:D man, that brings back memories, i know wat u mean, i can remember them note for note too! very funky, very well made!
now if only i could find a bass tab for it.....

If you look a bit you can find the entire soundtrack in mp3 format on cell phone ring tone sites.
I'm not sure of the legality, but somehow I don't think you'll be raided for it.

I absolutely adore video game music. I have about 20GB of it on my hard drive.
Some of my favorites:
Outlaws (best soundtrack ever!)
Zombies Ate My Neighbors (Genesis)
Wing Commander III
Crusader: No Remorse
Deus Ex
Ecco the Dolphin (Genesis)
LOOM
Super Dodgeball (NES)
Ghouls'n'Ghosts (Genesis)
Blake Stone: Aliens of Gold
As Skreczi knows, Still Alive is the most annoying song ever.

Stay a while, and listen...

Megaman (various games) songs
Mario 1,2,3 and world songs.
Sonic The Hedgehog 2 songs (didn't like 1)
Pokemon Battle Theme
Final Fantasy (various tracks from 1, 6, 7, 9) songs
yeah, I do a lot of humming/whistling and people get pretty annoyed.
Also, thanks to bands like The Minibosses, The NESkimos, and The Advantage, I also get songs from Batman 2 (NES), and Metal Gear (not solid) stuck in my head.

Final Fantasy winning battle music.
Zelda when you pick up items.
Two that I regularly use in convosation :P

Music-wise, anything Frank Klepacki (C&C, Bladerunner, UaW) composed has stuck with me. Deus Ex and its sequel, the Genesis Sonic games, Crusader: No Remorse, Starsiege, the main theme from Metal Gear Solid, and some others.
As for quotes...
"Believe what you want to believe, McCoy." - Bladerunner
"Power shifts quickly in the brotherhood." - C&C
"Kane lives in Death" - Tiberian Sun
"Sure (drawn out)" - Deus Ex (The way JC says sure has always been funny to me.)
Anything Duke Nukem says in DN3D

*CRRRCHHHHHHH-HHH-HH* (sound of identifying all items) :)
How about,
'What are ya sellin'?"

command & conquer red alert the music hit me when i first played it still plays well even now. Wonder what hells march 3 will sound like.

"What are ya buyin?"
"heh heh heh, Thank you!"
"Is that all stranger?"
lines me and my friends quote to each other, then laugh.
"You require more vespene gas!" (as protoss)
"Stop Poking MEEEEEEE!" from warcraft: orcs and humans
"Hurray! WOW! Yeah! Stupendous. Wonderful!"
"Chicken chaser? do you chase chickens?"
all comic lines, as for sound bites, the sound that the rings make when you pick them up in sonic, and the coins in mario.
all the music from sonic 2 is fun to hum, but the main zelda theme is what i like best.

From time to them the different ocarina songs from Ocarina of Time come to me randomly.
Also the battle music from Pokemon...