Do you know any? Dont count Sims because you cant finish this game :P
My personal choice is Arcanum. It is possible to persuade last boss to selfkill... Truly awesome game. And i would not mention Fallout, because you technically kill people, not directly but still (NPC kills count i guess).

I think you could finish Postal 2 without killing anyone.

I killed more than a thousand enemies on my Arcanum game (my character was a witch with no soul though).
Also, in Civilization games you can murder millions or not a single person (you'll probably end crushed by Stalin's iron fist though).

Portal, but then again, there's is really no one to kill in that game (the companion cube and GLaDOS don't count).

LOL
Lucas Arts Adventures.....That was easy.

The thief games. You knock opponents out instead of killing them, which just makes the game that much more difficult.
Also most racing and sports games.

You actually kill a few people in both Indiana Jones games and kill Lechuk in Monkey Islands (though he always resurrects).

Whenever I play racing and sports games I try my hardest to kill but it never works.

Nope. In "Thief," there's always some kind of major boss who you have to kill by sabotaging his/her/equipment. So, indirectly, you do kill people.
Most adventure games can be completed without murder...

The first two King's Quest games allowed you to kill certain people.
You do get more points for taking the pacifists path.

what about Grim Fandango?
Syberia 2 or one. one of them featured death and it is your fault. the other one doesn't.
Fallout 2. possible to finish the game without killing anyone/anything (and without your NPC killing anyone either) although one person will die because of your actions! (not possible tough if you don't know the game.)
what about planescape torment? did you have to kill anyone? the last boss as well as the angel. you could avoid fighting them.
Teenagent :)
Emergency
Theme Hospital (i think it is possible to not kill anyone but i have never done it :) )
Deus ex? You had a stun rod and atm i don't remember anyone who had to be killed for game to progress
any multiplayer game: you just let others kill you.
what about story mod of X2. did it involve killing anyone? You could force enemies to leave the ships (and then you could run the over with your ship or be more humane and enslave them :) )
Constructor
Wet the sexy empire: make love not war!
Capitalism 2 and other economic strategies
I believe Alpha centauri when playing as gaia faction. Probably very hard but might be possible.
does killing undead and hell spawns counts as actually killing?
cause diablo 1 would count as a game without a single death!
im out of ideas atm. will add something later.

Indy, you knock them out. Oh I forgot you crush that big buff guy with a boulder in Fate of Atlantis.
Le Chuck, is already dead. If something is already dead it doesn't count.

Except Thief 3 where the end boss just gets depowered.
Anyone unfortunate enough to be in or around the clock tower, however...
I could never resist throwing unconscious mechanists from the top balcony in Angelwatch.

In the Last Crusade you actually shoot down a few planes and in Atlantis you kill Sofia's keeper.