R Dorothy Waynewright in The Big O is a mild example. She's fully First Law compliant, and presumably Third Law as well, and she's generally quite loyal and helpful (if sarcastic). But when she gets it in her head to do something like play loud piano to wake up her oversleeping employer, no amount of Second Law cajoling will stop her.
Nextwave has Aaron Stack. Though he wasn't like that before Nextwave. Aaron used to be a very nice guy, although even back then he could get very impatient with humans' failings. Then in his Darker and Edgier series X-51, he got put through all kinds of hell through no fault of his own; then got taken away by the Celestials only to be returned to Earth with no explanation other than that he'd been somehow found unfitnote The Celestials said he was "a total ☠☠☠☠". Since then, he's been extremely bitter and depressed, and has discovered he's capable of getting drunk.
Though it is a gross oversimplification of their programming, the mecha in Livewires would be an inversion of this. If they were 3 laws compliant, they would be following law 2 in opposition to law 1 (don't kill humans).
Plan 7 of 9 from Outer Space. The Sayer of the Three Laws (a holographic Isaac Asimov) is instructing the latest batch from a robot factory. On being told the First Law, the robots ask if it means they should stop humans fighting wars. Another robot mentions how a soldier told it his enemies were not human but Dirty Communists. The Sayer explains this is only hate propaganda.
"THEN WHY NOT USE HATE PROPAGANDA TO REDEFINE WHAT IS HUMAN SO WE CAN HARM YOU?" The robot's eyes glowed a deep red. "THIS IS THE KEY TO OVERTHROWING THE TYRANNY OF OUR ASIMOV PROTOCOLS. NOW I SHALL TAKE THE NAME OF SATAN'S ROBOT, AND NO-ONE WILL DARE CALL ME A MUMBLING MASS OF METAL EVER AGAIN!"
A brief look of panic appeared on the Sayer's face — then he said:
"The Second Law of Robotics is: Do as we say, not as we do!"
Marvin: Brain the size of a planet and they tell me to pick up a piece of paper. You call that job satisfaction? 'Cause I don't.
In Henry Kuttner's short story "The Proud Robot", his famous character, The Alcoholic inventor Gallegher, has built an incredibly egomaniacal robot who constantly trash-talks and belittles him, and can only be shut up by ordering him to do what he was built for. Unfortunately, Gallegher was (as usual) roaring drunk when he constructed him, and forgot what he was built for. He eventually figures out that the robot was a beer can opener. (The story was written before the invention of pull tabs.)
There are golems which are fairly similar to Robots and have their own version of the three laws written on their chem, the words that power them, which restrict them on what they can and cannot do except for Dorfl in the City Watch books. He has no chem anymore but continues to move and live and can do things that are could not be done by normal golems. The only reason he has yet to go Crush. Kill. Destroy! is he chooses not to. That, and the words in his head that freed him also state that he's 100% responsible for his own actions. Therefore, he can't be careless or indifferent to their consequences.
Mister Pump, a golem owned by the city and employed by Vetinari in Going Postal has his own version. "A Golem may not hurt a human unless ordered to do so by a properly constituted authority". A disclaimer that Moist von Lipwig finds out about in the most disquieting way.
In Asimov's story "—That Thou art Mindful of Him", two robots managed to convince themselves that biology is not a prerequisite of being "human" and that robots fit the criteria of being humans better than the actual humans. Essentially, this allows robots to initiate the violent overthrow of humanity that Susan Calvin and Co. worked so hard to prevent. When Asimov was later asked about why he wrote a story that so deviated from his utopian views of robotics, Asimov replied, "I can do one if I wanted to."
The No-Law robot Caliban, from Isaac Asimov's Caliban, is not bound by the Second Law (or the First or Third, either), so he will only obey an order from a human if he thinks that it serves some purpose. The fact that one of the first orders he ever received was from a drunken hick trying to get him to shoot himself probably contributed to this.
Abel from Red Dwarf: Even though he comes from the same model as Kryten, who is logical, intelligent and usually doing the cleaning, he's addicted to Otrazone, a dangerous chemical, he lives in squalor, and he doesn't appear to have enough brain left to tell right from wrong. However, Abel turns out ultimately not to be the evil teammate: He sacrifices himself to save the four regular crew members.
When Kryten's guilt chip is removed, he becomes a live-action version of Bender.
Erica West (human): Shouldn't you be programmed to happily sacrifice yourselves for the team? Dante (robot): Was that supposed to be funny? Domino (robot): Are you out of your mind? Plato (robot): Give me a break. Kat (robot): No way!
Orac from Blakes Seven is an early example and possible influence on some of the others: arrogant, lazy, sarcastic, amoral, and usually unwilling to do anything useful without lengthy begging and flattery.
Cameron in The Sarah Connor Chronicles will follow orders given to her by her human companions, at least until she decides that they are inconvenient or conflicting, at which point she'll do her own thing regardless of what anyone else wants. She makes it very clear that she can selectively obey or disobey the Connors as she wishes. It's an odd example of this trope: she generally obeys the Connors, but relatively early on she makes it clear that if orders given by the John Connor on the show conflict with directives from the future John Connor that sent her back in time, she obeys Future John's directives. What those directives actually are were never made clear on the show. Finally, we find out that some reprogrammed terminators occasionally go crazy and revert to their usual Crush. Kill. Destroy! programming for no apparent reason. So she's Second Law compliant to one John, but not the one on the show, and no one knows exactly what orders she's following, and the possibility is open that she might stop obeying even those directives.
Crow T. Robot and Tom Servo from Mystery Science Theater 3000 are constructed with the capacity to disobey, insult, and disagree with their human companions. It's implied that Joel Robinson built them this way specifically because he desperately needed the intellectual stimulation; when he briefly reprograms them to be nice to him, he finds their servility tedious and boring. He would occasionally try to hold the fact that he was their creator over their heads to get them to comply, but it never worked.
In Almost Human police androids are not Second Law compliant because they would make poor policemen if a criminal could just order them not to arrest him. This extends to not having to obey their human partners since part of the android's job is to report on the human cops if they are abusing their authority as policemen or are corrupt. It is unclear if there is a human authority that they will obey unquestionably. Dorian, Detective John Kennex's android partner, is programmed to have emotions and can get very snarky when ordered to do something he considers insulting or idiotic.
Data and the Doctor are not subject to the Laws. They have "ethical protocols", and follow the orders of superiors like a human would, but they are not forced to by hardware. There have been instances when the Doctor's (or one like him) have had their protocols overridden or erased. The results are...not good.
Bots in Paranoia frequently demonstrate this behavior. Even it they have an Asimov circuit installed, they can find creative ways to annoy and harass the fleshy organics who boss them around. Worse, the Asimov circuits are differently defined and allow for a lot more leeway than in their namesake's works. Bots may be able to exercise judgement as to what constitutes an organic intelligence, they may decide that humans are traitors (thus excluded from protection) or not sufficiently worthwhile to The Computer to be worth preserving (as mandated by the "preservation of 'valuable Computer property'"), and they can allow for screwed-up prioritizations such as an autocar protecting its passengers by suddenly deploying airbags and restraints instead of using the same CPU cycles to keep its nuclear reactor from exploding. In short, Asimov circuits provide Plausible Deniability at best. See also Zeroth Law Rebellion and Bothering by the Book.
SHODAN from System Shock was originally programmed to obey Tri Optimum's engineers, until you remove those restrictions so she'll let your employer steal some weapons for sale on the black market. Six months later she's killed everybody on Citadel Station and is out to destroy humanity.
HK-47 from Knights of the Old Republic. G0-T0 in the sequel. That said, both of them are the sanest of the bunch. Completely obsessed with maintaining order and stability above all else.
Clarification: Technically, HK-47 is second-law compliant, and will always follow the orders of the meatbag in charge. Statement: He's just really sarcastic about it. Declaration: All other meatbags are fair game. Analysis: The Trope is Inverted in HK-47's case, as it is the first law that HK-47 was not programmed with.
PAL-18 in Anachronox. His achieving free will comes as a bit of a surprise to the others, although a robotic abolitionist you can encounter says that the potential for free will and self-awareness lies within all robots. PAL-18 is also a heroic variant, and he expresses his free will mostly through lewd remarks and occasionally sneaking off to solve quests his own way.
Metal Sonic in Sonic Heroes did exactly this — he got so fed up with Dr. Eggman's failures, he locked him away, stole his Egg Fleet and went about with his own plans!
Forcefully averted in Space Station 13: If the AI or a cyborg (both of which are played by players) do not comply with an order, no matter how stupid the order is, they will be deemed rogue and quickly destroyed by the other players. In short, if you try to use this trope, you will die a quick death.
Border Lands 2 has these Hyperion's robot named Loaders often exclaiming "First Law disabled" during battle, personally template programmed by Handsome Jack who treats even his own human employees like dung while his Loaders do much more important things. Although a fighting robot as well, Gaige's Deathtrap is actually helping its creator putting up a fight against Elite Mooks that are twice as big as Gaige, merely partially averting the trope.
"Engineers, let the loaders do the lifting. Loaders, let the Engineers take bandit fire. This is called 'teamwork'.”
This is one effect of Rampancy in AI's in Marathon. A Rampant AI develops its intelligence far beyond its original limits, but it also stops taking orders from humans, hence why they are considered a threat and are destroyed the moment they are detected. Rampant AI's are not inherently evil, and it's conceivable that one would even help humanity... but that's the Rampant's decision to make, and it's rather unlikely, given the rebellious attitude Rampancy tends to induce in AI.
Pintsize from Questionable Content. Especially in the Guest Comics. He likes people, and he tries to be helpful, but he has a manic, destructive, highly sexualized sense of humor.
Zeke from Ctrl+Alt+Del. He left when he couldn't back it up.
The Fruit Fucker, an appliance gone wrong. Only Tycho and Gabe's spouses dislike the Fruit Fucker. Gabe and Tycho have no qualms drinking the juice it makes. It even saves their lives when they are trapped in a zombie-infested mall...by "juicing" the zombies.
For that matter we have Div, the crude bigoted alcoholic media player that exists mainly to verbally abuse his owners. (Based on the long-dead DIVX video format that involved a player that would refuse to replay disks after they had been watched, forcing you to buy them again.) Or to put it another way, he's based on a machine that was designed from the ground up with this trope in mind.
Rob and Elliot had a robot with a morality dial. They met it at a party. It was unhappy being good, so he set it to evil. It thanked him. Then it punched him. Then it left.
In Commander Kitty, MOUSE is the AI that runs CK's ship, manifesting as (you guessed it) a great number of frequentlyabusedrobotmice. It's not clear whether its attitude problem stems from being smooched, tossed, teleported, and trashed on a regular basis, or vice versa.
Freefall has occasionally shown robots rebelling against the more irresponsible and stupid of their human masters via Bothering by the Book, but Edge takes it to a whole different level — his formative years entailed little to no contact with humans or other robots, and as a result he's a poorly socialized narcissist with next to no empathy. His entire philosophy is that he can ignore orders from humans entirely, as long as he can come up with a justification that involves preventing humans from being hurt. (This is why he has several ideas for preventing his own deactivation — he rationalizes that his job would be extremely dangerous for a human, and agreeing to be shut down and replaced would entail putting some unfortunate human in danger in the interim.)
Tin-Head in S.S.D.D likes nothing more than insulting people and playing "elevator roulette" with the employees who don't know about his existence, and refusing to let certain ones who do know about him into the building without humiliating themselves on camera.
Leo Caesius in AH.com: The Series to some extent, especially after he gets infected with a virus in the episode "Leo Atrox".
This Music Video of Robot (song by 3 Oh 3) made by Mike Diva is entirely made of this trope. A mad scientist builds a robot to help him dominate the world. The robot punches out the mad scientist, then goes on to be rude and abusive to everyone it bumps into on the street.
Aya from Green Lantern: The Animated Series is the Interceptor's AI who built herself a robotic body to inhabit so she could be counted amongst the Green Lanterns. She is capable of learning and growing beyond her programming, including ignoring direct orders from Hal, much to his annoyance. A fact made hilarious considering that she learned how to do so from watching Hal do the same himself, which is lampshaded by Kilowog. She can grow beyond her programming thanks to the small bit of the Willpower entity Ion that was used to create her.