Shadow of Rome actually rewards you for finding out just how many different ways you can kill someone in the arena. Force them to wet themselves by holding an arrow to their head and then shoot them while they pee themselves, hack off an enemy's arms and legs, then beat him to death with a limb, push enemies into fire traps and then throw the switch to incinerate them, push enemies into spike pits, duck underneath spinning blades and trick enemies into walking into them, smash their head with an iron ball and chain, kick a guy in the junk when their back is turned... There's well over 100 different Salvos for you to find, which means over 100 different ways to kill an enemy. Chop an enemy's head off and throw it into the crowd. They go absolutely nuts and cheer you on harder and give you health items and better weapons.
God of War Series is perhaps the king of this trope, as you can kill your enemies in ways that don't bear repeating; hell, one of the basic moves is to rip enemies to shreds with your bare hands. In fact, if you don't do horrible things voluntarily, the game will make you do them.
There's a very specific scene early on in Athens with Ares attacking the city proper and citizens fleeing around chaotically. The game rewards you with health for killing them.
In Pandora's Temple, one puzzle is solved by you lowering a suspended cage holding a soldier and, instead of freeing him, pushing him uphill to a machine that incinerates him. He pleads with you and shouts for help the whole trip, of course.
There's also one section where you're on one side of a chasm, and the only way across is to pull the lever on the other side and activate a bridge. Naturally, there's a civilian who'd be all too happy to pull said lever, but he's too terrified of all the monsters on your side. Pop quiz: how do you get across? Answer: Zap the civilian with lightning. His dead body will fall on the lever and allow you to cross.
And don't forget the sequel, where — not once, but twice — you must drag a helpless and protesting old scholar towards a book so that he can read it for you. Once you get him there, you brutalize him until he does what you want, then kill him. The real cruelty here lies in the fact that the game uses Quick Time Events (i.e., button-mashing) to literally force the player to put some real physical effort into this act of elder abuse.
Along with a scene where you have to kill an Argonaut by dropping him on a conveyor belt leading to a crushing wheel.
The third game ups the ante, by forcing you to drag a screaming and begging woman to be horribly crushed in a wheel... all so he can prop up a door. Why Kratos doesn't just use one of the very plentiful enemies in the area instead is completely unknown. What makes this better is that you brutally murdered her husband earlier in the game.
And the poking his eyes out part? It's one of the very few times in any video game where the action is viewed from a second-person view. Yes, you get to watch Kratos' (and your) brutality from the viewpoint of the victim.
There's also ripping off Helios's head with your bare hands, THEN USING IT AS A LIGHT SOURCE. The scene of Kratos ripping the poor Sun God's head off was so graphic that X-Play was forced to censor it...but the studio launched into so many "OHHHH!!!"'s that every viewer could tell what was happening.
At the very end of the third game, the fight with Zeus is ended off with a button mashing section where you're just punching Zeus's head in. Over and over again. You can do this as many times as you want before killing him, and it feels so damn satisfying.
Dante's Inferno has you punish or absolve the sins of the people and monsters you meet in hell. It is also, in some ways, a clone of God Of War, so similar examples to that game above abound.
Long-forgotten PC title Die By The Sword was made with this very much in mind. The game gave you considerable control over your character's sword arm, allowing you to sever heads, arms and legs as you saw fit. The interesting thing was that you could sheathe your sword and pick up these severed body parts to use as clubs. Even better, cutting off a limb did not necessarily kill the enemy in question, making it entirely possible to beat an enemy to death with its own leg as it hopped about madly trying to avoid you. The expansion also included a special 'ogre hockey' mini game that allowed you to control a lumbering, club-wielding brute trying to score goals against his opponent — using a kobold as the puck.
In some Dynasty Warriors games (#5 in particular), there's nothing preventing you from standing in front of a gate and killing everything that wants to come out. Gate guard too busy fighting some other random troop? Kills can easily go into the thousands from the gate alone. Which is how you're supposed to get Lu Bu's ultimate weapon. Even for a game where your reasons for fighting means the end to a two- to three-generation civil war, this is kinda cruel.
The battle of Chang Ban on Wei's side encourages you to target Liu Bei's peasants. In most games, this results in a heavy morale loss among Liu Bei's troops, resulting in the level being easier to beat. In 6, Liu Bei won't even bother to fight you unless you kill at least one peasant leader (and fighting a leader heading straight for the escape point is more difficult than it sounds). On the other hand, killing all of the peasant leaders will piss Liu Bei off enough that he won't bother running for the escape point (though if he gets anywhere near Cao Cao and you're not near him to protect him, that's pretty much an automatic game over). On the flip side, losing all of the peasant leaders on Liu Bei's side means instant defeat.
Pretty much the point of the The Suffering. As an inmate in a prison attacked by monsters, you're given the choice of helping out fellow inmates and innocent guards who are in trouble. It's entirely possible to watch them die in misery (or kill them yourself), but it affects the plot. Saving them changes things as well.