Is it really possible to finish Deus Ex without actively killing a single enemy?

Actually, yes, and I believe it even extends to all of the bosses. If you stick to tranquilizer darts, gas grenades, batons, and stun guns, you can get through most fights without actually killing anyone.

This is really easier said than done though, since non-lethal ammo is very limited, and you'll find that the some of the boss fights are nearly impossible.

If you're going to actually try this, sneak past as many guards as possible, conserving ammo for when you really need it.

It can in fact be done, and here is a step-by-step walkthrough proving it.

http://www.visualwalkthroughs.com/deusex/deusex.htm

Be aware that getting past

Anna Navarre

without killing her requires the use of what some would call "finesse" and others would call "AI exploiting".