Here's all the games I can think of with non-lethal options, many of them revolving around stealth:
Dishonored reacts in a very, very simplistic way to how many people you've killed. The process of actually KOing people instead of killing them is almost entirely cosmetic though, just plays a different takedown animation.
- Metro 2033, Last Light and Exodus all have a karma system where not killing anyone will set you up for the best endings. In the original games you had to sneak by, but in the Redux games you can KO people, which is identical to killing them except for the animation.
- Thief enables you to slip past everyone or KO them with the comically-overpowered blackjack. Blackjacking someone renders them essentially dead for gameplay purposes.
- Mirror's Edge has an achievement for never killing anyone, but no in-game reactivity beyond that. The actual non-lethal gameplay amounts to just voluntarily not picking up guns or kicking people off rooftops.
- Desperados 1 and 3 enable you to clear the whole game with no kills at all, but the game doesn't really react. That said, the gameplay mechanics change if you attempt this and the game becomes a lot more difficult, so it's actually one of the better non-lethal playthroughs in a videogame, especially in Desperados 1 where only one character carries the rope necessary to tie enemies up, forcing you to radically change your plans to ensure that he's always got access to the most recently KO'd enemy.
- Hitman games encourage you to never kill anyone other than the targets, which can be a lot of fun as it requires what people call "social stealth". You could argue the game reacts since if you fuck things up and cause chaos, everything spirals very quickly out of control.
- SWAT 4 strongly encourages you to never kill anyone, which does tangibly change the gameplay in that you have to announce your presence to people who are very likely to open fire on you, and then you must shoot to wound (or use laughably underpowered non-lethal weapons).