Like in Stalker where the mutant dogs will turn tail and flee if they take too much damage or if you kill enough of their pack members. Red Dead Redemption's animals also ran away if a fight wasn't going their way.
Actually, Rockstar games are pretty good with this sort of stuff in general. I'm pretty sure you could shoot guns of of people's hands in RDR to make them put their hands up, or cause a fatal gunshot wound that would make them crawl around on their belly and call for help. Both GTA 4 and 5's enemies have injury states where they will take potshots at you with a pistol while bleeding on the ground or just passively clutch their wounds until they die.
I guess it wouldn't work in arcadey or linear games where the point is to kill everything on screen, but for anything more open-ended that tries to go for something approaching realism it'd be nice if the enemies you faced felt more alive and/or showed some basic survival instincts.
DayZ and some similar games have surrendering as sort of a player cultural convention. What actually happens when you surrender depends on the players - Some people are assholes about it, but others will politely rob you, and a lot of times people end up joining and working together after one of them gets captured and they have a chance to talk.