Thief the Dark Project and Thief 2: The Metal Age. Both are considered the best stealth games, and Thief was basically the creator of stealth FPS games.
For the most part, nothing, the guy just ends up dead. In some missions though, you lose if you kill someone. The way the game tries to discourage killing is by making enemies actually tough to fight, and facing 2 or 3 is most of the time death.
You should try them, you'll probably like them a lot. The only problem is that they are a pain on modern computers.