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.
Shadowrun at least recommends not just up and murdering people, even when fighting, on the reasoning that racking up a body count is a good way to draw the wrong kind of attention to your band of professional criminals. It also has plenty of alternatives and some expectation that you might neutralize a threat with one shot without actually killing them, because of composure tests. It also discourages players from killing in the nastier ways like mind control.
Icon (Lancer, but fantasy instead of mecha space opera) is still being worked on but that explicitly states that sapient enemies should probably open with threats rather than actual combat and that they should flee or surrender when combat doesn't go their way. I can't remember but I think it mentions living enemies in general being more likely to flee that to fight to the death as well.
Depends on the shadowrun and the stakes, I've found, and how much of our faces they've seen.
Can't just go shooting up the place if the place has a contract with Knight Errant or Lone Star. In Ecplipse Phase it's often Direct Action - If you cause enough noise for someone's security contract with Direct Action to activate you'd better hope you have a near by exit or some really big guns.