PAIN is about firing people at buildings and billboards with a giant slingshot. Cruelty and, well, pain are the entire point.
The Incredible Hulk: Ultimate Destruction. Considering that the main protagonist is the embodiment of Bruce Banner's suppressed rage, it's no surprise that the player gets to do some pretty mean things. Players can pick up policemen, soldiers, and absolutely defenseless civilians alike and beat them up, throw them from buildings, into the sea, or traffic. Speaking of which, all cars, clearly driven by mere passers-by, can be picked up, destroyed, thrown, or crushed into metal gloves, whereas buses can be crushed and used as surfboards. Several buildings can be destroyed, different destructible objects piled up for bigger explosions, lampposts can be turned into clubs... In fact, there are several side-quest minigames that make a pronounced point out of cruelty. One particularly noteworthy example is using a metal girder to bat soldiers away for distance records. On top of all of that, one unlockable changes the Hulk into his gray "Mr. Fixit" incarnation, who gleefully throws out one-liners about the suffering he causes.
Hitting people with a lamppost makes a very satisfying "PONGK!" sound.
The giant fighting robots the military sends to fight you can get not only IMPALED with the lamppost, it can pin them to buildings. Watch the operators inside struggle to unpin themselves before their robots explode with glee.
The Hulk actually has two special moves he can use when holding civilians. One has him putting the civilian down and patting them on the head. The other has the Hulk flick the civilian and send him flying. You can also do a dramatic elbow drop while holding someone. While it doesn't hurt them, it seems cruel to basically pile drive some random person off the tallest skyscraper there is.
Notably, that special move where the Hulk gently puts the civilian down and pats them on the head can be turned into one of the crueler things to do in the game; they will always run away from you screaming after you set them down. Always. Even when you set them down on top of skyscrapers, they will run away off the top of the building and fall to their deaths.
And that means ALWAYS always. For example, if you pick up the broken body of a hapless civilian which you have just finished smashing before they disappear and put them back down with a gentle pat on the head, they will revive, leaving them vulnerable to more unspeakable Gamma-fueled cruelty.
Like the Spider-Man example, you can pick people (or mecha) up and then piledrive them off a skyscraper and into the street below. Even better, Hulk's piledriver is a chain throw, meaning you slam the poor schmuck into the ground, bounce up into the air, and repeat for as long as you can keep the combo going.
For once, this trope is justified until the last two missions by the character of Devil Hulk, a being in Banner's mind who compels the Hulk to wreak even more chaos than usual; one of the goals of the game is to fetch the parts for a machine that will allow Banner to enter his own mind and deliver a smack down to the Devil.
In LEGO Batman (and assumedly the other LEGO games), you can beat up your allies. Including Alfred. The temptation to wander around the Batcave beating up the various batfolks is almost overwhelming. The Batcave is also possibly the most dangerous area just because nothing has handrails and it's incredibly easy to either walk off the edge or 'accidentally' push someone off. And then you go to Arkham... and the fun noises the various rogues make when you beat them up — with other rogues. Plus of course, having Poison Ivy destroy every plant she can.
In order to get the "Superhero" rating for the hero storyline, you have to get x number of studs per level. In order to do that, you have to break things. Ergo, Heroism = Vandalism. Breaking things equals FIGHTING CRIME.
In LEGO Harry Potter, Dark wizards have Avada Kedavra on their spell wheel. And can go around casting it on anyone they like, including enemies, allies, Muggles...
In Ultimate Spider-Man, you get to run around as Venom and basically wreak cruel, cruel havoc — including throwing cars at bystanders, snapping their spines, and literally draining the life out of them until they're reduced to shaking and lying in a fetal position on the street. It's... oddly satisfying after a hard day.
In the game of the first movie, there are several levels where you're hunting gang members on rooftops. One of the elementary moves (alongside tying people up, which can often qualify for this as well) is to snag them with webs and yank them over your head. Combine this move with the natural property of roofs to include precarious edges, and you've got a party. Bonus points for your mission radar (which includes an 'elevation' bar) tracking the descending gangster on his short trip to the ground.
Then there's the second movie game, in which you can pile drive bad guys off the Empire State Building.
You can also throw them into the ocean, off of a building (though much less exciting than pile-driving them off the Empire State Building), or into other bad guys. Add this up to the numerous hideouts and Bad Guy Bars...
In Mirror's Edge, your character doesn't carry any weapons and can only use the weapons of disabled enemies until the magazine is empty, so most of the time you just beat them unconscious or, which is an even better idea, just run away. As all the enemies are cops and the entire plot of the game revolves around saving the main character's sister, who also is a police officer, it's also easy to consider them not deserving to be killed at all. But at the same time, almost all of the game takes place on the roofs of very high skyscrapers, with cars and people appearing only as tiny dots on the ground far below. Let's just say that none of the roofs have handrails.
Pursuit Force is a Cowboy Cop action game series that sometimes goes too far from cheesy and fun. When you switch into a gang vehicle, you do not subdue the driver or ask him or her to move over; you just shoot the sucker and toss the corpse out when you enter. If you are taking over a motorbike, you will wring the biker's neck and shove him or her off. Oh, and if the car you took had passengers, you have to kill them all too before taking over. Afterwards, you can enjoy the wonderful 3rd person view of still-bleeding stiffs merrily swinging in the car beside you.
You can only arrest enemies on several infantry battle missions (which are pretty brutal and modified from Dead to Rights: Reckoning's execution scripts), and you are not given any non-lethal firearms or devices. Most of the time, you must "neutralize" them via a faceful of bullets.
The early 80s Lucasfilm game Rescue on Fractalus! had you flying around a hostile planet in your space fighter, rescuing friendly pilots stranded there. However, if you weren't interested in actually rescuing your comrade, there were plenty of ways to kill him instead, such as turning on your fighter's engines when he's outside (instantly incinerating him), shooting his crashed ship while he's sheltering inside it, or refusing to open your airlock when he knocks to be let in (the acidic atmosphere of the planet eats through his spacesuit and kills him if he stays outside for more than a minute — you can actually hear his knocks getting fainter and feebler as time passes).
In Stampede Run, you can knock other runners out of the way, either by sweeping them with a slide or bumping them from the side.