Only one character had to actually die in order to finish Deus Ex (all others--including monsters and other non-humans--could be avoided through trickery, stealth, invisibility or just running away, although of course it was easier to use lethal or non-lethal weapons on them), and that character was able to be killed through a special, indirect manner without using any weapon; however, this hands-off option only opened up if you had previously obtained the necessary information.
I very much doubt hands-off completion was possible in Invisible War, especially since the endgame required people to die (although not necessarily by your own hand) and all maps were so tiny that there were few options for hiding or evading most enemies.

You can in Sims 3 as your Sims die. :)
I haven't played much, but Hotel Dusk doesn't require killing I think, and that is a fine game. I also recall Hideo Kojima saying Metal Gear Solid 2 could be finished without killing (just using the tranquilizer I assume). Just a couple off the top of my head.
Edit: how could I forget? Mirror's Edge. Pretty sure you don't have to kill anyone..you don't have to use guns, anyway..except one part..

There's actually a Mirror's Edge achievement for not killing anyone the entire game. Friend has done it on Hard. I can't even imagine such a thing.
Planescape: Torment will eventually lead to you having to kill something, in a number of ways.
I can't really think of anything else at the moment, except perhaps the Descent series if we're going by either A. Sentient creatures or B. Humanoids

Mirrors Edge is a definite no killer game, there's an achievement for it in the 360 version. There IS one certain death at the end but thats out of the players control so they could at least claim diminished responsibility
*SPOLERS FOR MASS EFFECT AND KOTOR2*
Its not so much comitting suicide in ME , its more reminding Saren that he doesn't have much in the way of free will and if he doesn't resist he'll just be a bitch all his life, then HE decides to top himself. I can't speak for anyone else but I was expecting him to run off, be killed by soverign or possibly join you for the final fight. Topping himself was cool in a dramatic manner but was sort of disappointing, I was hoping for another Aribeth situation where you might actually be able to defend him this time.
You can do much the same in KOTOR 2 with Darth Sion, basically remind him that he's been a bitch for ages and that he really doesn't like his life so he should just let go

It's been a while, but can't you just hit the guy in the missile silo with a tranquilizer dart?
In Invisible War, nobody has to die if you choose the ApostleCorp ending. Opposing factions may fight amongst themselves, but that's hardly your fault.

can you remind me who must be killed for you to progress with the game...

I ALMOST did it on hard but the last few levels just got too damned difficult so I decided to chuck it in, disarm the first bloke I saw with an M60 and gun down everyone I saw. Later got the no kills thing (technically no gun kills but the only other weapon is martial arts which is probably non lethal) on easy
PST has some compulsory killing, there's a few sections where it seems you just can't avoid it (I think at least Ignus/Vhailor and Trias are unavoidable fights) but you CAN talk the final boss to death which is nothing short of awesome.

I'm pretty sure there's no way to get around the fight with either Ignus or Vhailor in the Fortress of Regrets.
EDIT: Beaten by just minutes. But a fight with Trias can be avoided.

Im quite sure you can skip killing Trias...
and you don't need to kill either ingus and VHAILOR

The only way I can think of not having to kill Ignus would be to not have him in the party in the first place. I had him in my party and he went all psychotic (well more than he already was) and I had to kill him. No amount of talking got me out of that situation except for killing.

One of them will show up regardless of whether they're in your party, so unless there's a way to run off without finishing them I don't see any way to avoid killing whichever one shows up.

It's been ages since I played it, but I believe there is a point in the game which causes Ignus to attack you regardless?
*Brain wave*
Right, yes. If you've acted mostly Lawful Good/Neutral (which not offing people contributes to heavily) Ignus tries to 'light your fire', as it were, in the Fortress.
So you aren't required to kill him, but if you've been taking a lot of non-violent routes, it generally ends up there.

I gave up on attempting a no-kills game in Mirror's Edge; there was far too much trial and error.
I felt somewhat vindicated when a cutscene near the end had Faith murder a bunch of security guards. God, that would've pissed me off so much if I'd still been trying to keep her as a good guy.

Thx for explanation about PST. Didn't remember that part....
no wonder.
I just checked gamefaqs and was reminded how MASSIVE that game was. no wonder it took me over a month to finish it.
so one kill in game of 80 hours. not bad :)

No, I was referring to a person you face while visiting the UNATCO HQ for the very last time. That person must to die to proceed, and while earlier opportunities to kill this person are optional this last one is not. While it is technically possible to get around this kill by exploiting AI behaviour the game still considers this person to be dead.
It's interesting that there is a bloodless way to finish the Invisible War endgame. I only bothered doing the "true" ending within the game and then watched the videos for the others.