The original Splinter Cell comes to mind. You were supposed to be a stealthy spy, so killing was often counter-productive to your goal. But if you were really careful, you could go beyond that and opt to not commit violence at all, by thinking of the best way to sneak past, trick, and divert your enemies.
Putting aside the morality of it all, from a challenge/fun perspective, games make it all too easy to kill, but so much more difficult to avoid it. But some of the most satisfying experiences can come from thinking about the perfect strategies to not kill your enemies.
It is curious though, why so many games require killing/violence to be fun, when there is arguably a lot of untapped fun and new strategies to be had without those mechanics.