In Harvester, you can kill anyone. ANYONE. Beat your mom to death with a pipe? Sure. Go for it. If you kill someone before entering The Lodge, you will be executed. After The Lodge, however? Kill the nonessential characters as much as you damn well please.
In Snatcher, Handsome Lech Gillian Seed can flirt with almost every woman in the game, walk in on Jean Jack Gibson's daughter while she is showering (and she was 14 in the original JP version of the game; chances are her raised age in Western countries was due to how Squicky the scene could be.), force a Robot Buddy to watch a porn movie, and go to a strip club. The problem? Gillian is married.
Gillian has nothing on his Spiritual Successor, Jonathan Ingram, from Policenauts. Gillian can hit on every woman. Jonathan can outright molest every single woman in the game, including fondling the breasts of every single female character. The remake for the Sega Saturn actually upped the amount of Fanservice "due to popular demand."
In updated rereleases of The Secret of Monkey Island, one Xbox Achievement/PS3 Trophy requires you to let Guybrush drown. Gee, thanks for making me feel guilty just for a virtual reward!
You could already do that in the original PC release, and many people did. Some did it by accident, others did it on purpose because their friends had told them how they did it by accident.
Both Little Big Adventure games pretty much allow the player to attack anyone. Some of the NPCs can even be killed (only to come back later once you leave the area), and some of them will fight back. Note that most of the friendly characters can't be hurt, but if they fight back, you do get the damage. In particular, try beating up the kids near the beginning of the second game when it's still raining, then go outside and watch an... interesting cut scene.
The second game also has some locations that allow for creative ways of killing the Franco guards. One can be lured onto an electrical bridge while it's turned off and fried on it by pressing the switch in time (complete with X-Ray Sparks). Another one can be tricked into following you into the space suit chamber on the Emerald Moon and sucked into space when you put the suit on, opening the gate.
There is one part of Zak McKracken and the Alien Mindbenders where you have to raise hell on an airplane to loot the crucial stuff you need from it. First off, you plug the sink up with toilet paper and call the stewardess. She quickly shouts "Oh no!!!" and starts cleaning up the mess. Then, in order to keep her completely distracted, you go to the microwave...set in an egg and then BOOM! The stewardess then asks what the awful smell is and notices the microwave on the airplane is a mess. "AAAAAIEEEEEE WHO DID THIS?!" Poor stewardess... Zak would end up on Not Always Right for that!
You can also kill animals in inventive ways (Bludgeoning a squirrel, running a fish named Sushi through a garbage disposal.) Unlike tormenting the stewardess, these are optional.
Subverted in the sequel, Day of the Tentacle; Laverne revives the frozen hamster in a 22th century microwave oven, while delivering a Fantastic Aesop. (She explains that in her century kids who microwave their hamsters are taken away and put up for adoption, so don't do it.)
In the flash game Haunt The House, your goal is to scare everybody out of the house; you're warned not to freak them out too much, or else they may "do something stupid" (i.e. jump out of a window and kill themselves). Judging from user comments, quite a few people have finished the game by deliberately killing everybody.
In Sam & Max: The Devil's Playhouse, you have to use ventriloquism to distract the Samulacra — you can have Max throw his voice into a warehouse, making the Samulacra assault the door. Or you can use ventriloquism to have them assault Bluster Blaster or Sal, depending on who you like least.
There used to be a list of evil actions you could take in the Quest for Glory series, titled Quest for Evil by the discussion board members that came up with them. They included such things as killing the unconscious EOF opponent when told to in QFG2 and stealing coins from the musicians in QFG3 and 5. In 5, the musician would even thank you for stealing by playing a song for you.
In the Pac-Man 2: The New Adventures, you do not control Pac-Man directly, but act as his offscreen helper, guiding him along and helping him achieve his various goals. It is very possible to put the poor guy through a lot of suffering. Some of it is unavoidable, like where you have to induce a crow to attack Pac-Man in order to knock down an out-of-reach item. The downside to tormenting him is that he'll start ignoring your cues and you won't be able to proceed further until his mood improves.
In the Tex Murphy classic The Pandora Directive, you can choose to be a complete drunkard who treats everyone like crap, helps nobody but himself and only cares about getting paid. Many people get killed if you do so. Pretty impressive for a game with FMV cutscenes.
In Superbrothers: Sword & Sworcery EP the only way to get the Moon Key requires chasing down the bear/boar creature in the dreamworld, cornering him in a tree, and beating him into submission. Then you have the option of executing him while he is unarmed, beaten and gravely injured(but you get the moon key either way). It comes across as a particularly Jerkass move considering the creature does nothing to threaten you(or anyone else), spends most of it's time doing a wierd little dance, will actively run away from you when you get too close, and only draws a weapon when you corner and attack it. You can also Murder rabbits by making them explode, which you derive absolutely no benefit from.
Point and click game The X-Files Game has many ways you can cause trouble to people around you. You can be a total asshat to people by giving mean replies, ringing the bell at the motel several times to piss off the receptionist, asking the same questions over again after getting the answer to them already, etc. You can even go a step further by arresting people you're not supposed to, kill innocent people, or even killing yourself. These methods will result in a game over however.
In The Walking Dead, the player is given default guardianship of a young girl named Clementine, who has been on her own since the start of the zombie outbreak. Her parents are missing and presumed dead, and the only person she's had for company is a zombified babysitter, which leads to the potential for an player to do all kinds of mean, nasty, and downright cruel things to her that will further degrade her already questionable sanity. Gore and guts can fly in her presence, along with swear words she learns and repeats down the line. It gets to the point of brutally murdering people in front of her eyes. In Episode 2, the player can refrain from stopping Clementine from eating human flesh, served to her by the family of cannibals.
In The Legend of Kyrandia III, Malcolm can hypnotize a squirrel to wear it as a hat, put a squirrel through a machine to turn it into a leather ball, or make a squirrel paste sandwich out of it. Even though the squirrels aren't exactly friendly in that game (click on them too many times and they kill you).