Picard: What I am about to do is a direct violation of our orders. If anyone objects, please do so now. It will be noted in my log. Data: Captain, I believe I speak for everyone here, sir, when I say... "tohellwith our orders."
In Devil's Due's G.I. Joe vs the Transformers, the Joes defy orders to capture Wheeljack and Bumblebee, who were already working with them, and take them to Area 51 for study when they find out that the nukes the government plans to hit the Cobra base with are going to have an adverse effect when combined with the Energon that Cobra is trying to produce.
Heck, under Larry Hama's pen, the Joes regularly went against orders from more corrupt organizations like the Jugglers in order to do the right thing instead. One story arc even featured Destro saving the Joes after they were framed by a corrupt General.
The Animated Adaptation had Destro do so during the "Synthoid Conspiracy" two-parter when Cobra Commander had the Synthoids impersonate Duke and other military figures, as well as Congressional Budget Committee members (in an effort to undercut G.I. Joe and disband it). It failed miserably when the Commander tried to make a Synthoid of Destro and made the real Destro believe the Commander went that one step too far.
This is Batman's thing. The entire point of him dressing up like a giant bat and haunting the night is because he would never get anything done playing by the rules. Especially when the rules are made by corrupt officials who are connected to criminals.
Doesn't matter what the press says. Doesn't matter what the politicians or the mobs say. Doesn't matter if the whole country decides that something wrong is something right. This nation was founded on one principle above all else: the requirement that we stand up for what we believe, no matter the odds or the consequences. When the mob and the press and the whole world tell you to move, your job is to plant yourself like a tree beside the river of truth, and tell the whole world — "No, YOU move."
Most of the anti-registration superheroes in Civil War.
The dawn of the Bronze Age pretty much happened when Hal Jordan, following a lecture from Green Arrow, disobeyed the Guardians' orders and set out to stop a crooked businessman who was putting poor families out on the streets.
This is a fairly common theme in Green Lantern, period. The four human lanterns, and often a number of the alien ones, will go against a direct order from the Guardians or their Justice League teammates if they believe it will serve a greater purpose. Kyle Rayner sends a prisoner to Zamaron instead of Oa, John Stewart tells Batman to shove it when Bats disrespects Hal, the aforementioned Hal Jordan example, and Guy Gardner...well, he's freaking Guy Gardner.
In Destiny, Lauren disobeys an order from the Ash by helping a pregnant Fae come to term and delivers the baby. Unlike most other examples, there are serious consequences: the Ash throws Lauren in solitary confinement, but only after having some thugs beat her within an inch of her life. Despite the permanent physical discomfort, nightmares and psychological/emotional damage, and partial loss of movement in an arm, Lauren comments that she would do it again.
Lord Shojo of The Order of the Stick felt the restrictions on the Oaths that prevented them from seeking out the other Gates were too restrictive, especially since two Gates were destroyed within the last 20 years. However, his plans all involved disregarding his Oaths, going behind the backs of his paladins, and contacting foreign mercenaries. While Shojo is portrayed sympathetically, Rich points out that Shojo never considered trying to convince the paladins that the Oaths were outdated (plus, one of the locations was heavily booby trapped in case Soon or his followers decided to do this, the trapper believing this trope in the hands of paladins would only be a self-righteous justification).
Miko actually said the phrase "The laws have no meaning... Only honor and the will of the gods matter now". Granted, it turned out that she was doing the wrong, incredibly stupid thing, but she was convinced that killing Lord Shojo was the right and necessary thing to do.
Iron Man: Armored Adventures: In the episode "Fun with Laser", Iron Man goes against Nick Fury's order to stop the Living Laser and save the SHIELD space station after Nick's first plan fails spectacularly.
Pretty much Pepper's reason for every plan of hers, despite some plans including destroying the enemy's entire company.
In the Star Wars: The Clone Wars episode, Cat and Mouse, Anakin decides to engage Admiral Trench after he sends bombers to bomb the command center where Bail Organa is, because Anakin wants to not have Obi-Wan risk his fleet by engaging Trench, because he has less resources, and would be walking into a deathtrap.
In Disney's The Hunchback of Notre Dame, Frollo orders Captain Phoebus to burn down a windmill — with a couple and their two children locked inside of it. When Phoebus objects, saying that he was not trained to murder innocent civilians, Frollo starts the fire himself. Phoebus promptly breaks into the windmill to get the family out safely, and is arrested immediately afterward. Frollo comments on how he expected better from such a decorated officer.
In one episode of Popeye And Son, Popeye and his son are in a father/son contest, and one of the rules forbids the use of spinach. They end up breaking this rule when they have to save Wimpy and his nephew.
In the Family Guy episode "Screams of Silence:The Story of Brenda Q.", police officer Joe was initially against Quagmire's suggestion that they kill his sister's abusive boyfriend, since it would be murder. But when he witnesses the abuse for himself, his response is...
And in "Thanksgiving", a flashback shows Joe chasing a homeless man who stole some food, but he lets the guy off the hook when he sees he stole it to feed his starving family.
In The Avengers: Earth's Mightiest Heroes, Captain America suspected something was mind-controlling the Hulk to go berserk, who was currently captured by SHIELD and General Ross. When nothing could be done to convince them to let the Hulk go, he then proceeded to break into the underwater base and broke all sorts of rules to rescue Hulk, which was against his otherwise extremely lawful persona.
Hal tends to do this in Green Lantern The Animated Series, much to the annoyance of his bosses, the Guardians (save Ganthet, who seems to follow in Hal's belief in this). Lampshaded by Kilowog when Hals shows annoyance at Aya for doing the same after learning it from his example.