The Heretic is a traitor to The Church and/or its Canon. Most commonly, he was once a member of its congregation or even its clergy but got officially excommunicated for propagating beliefs that go against The Church's official dogma. Often, the Church sends out Knights Templar to Kill Them With Fire along with witches. Just being a heretic doesn't mark you evil by default: A heretic to a Saintly Church is often Chaotic Evil, but a heretic to a Corrupt Church or a Path of Inspiration may well be a Defector from Decadence.
To qualify as a heresy worthy of condemnation, the "heresy" should have an intrinsic connection to doctrines of the church in question. Someone who merely disagrees with the Church as an outsider is not a heretic - for instance, Hypatia of Alexandria. Wiccans and Buddhists are not considered "heretics" to the Catholic religion, but Padre Ned Reidy was put on trial for heresy.
The word "heretic" is from a Greek word meaning "to choose," so a heretic can be thought of as a person who chooses his own path. Christian theologian Irenaeus popularized the word heresy in the Christian world in his anti-Gnostic tracts. Multiple heretics often form a Cult.
Lenard and Elfetine's sect in Scrapped Princess. However, their "heresy" was provoked by Lenard, who is a (overly ambitious) cleric himself, in the first place.
Heresy is a common charge leveled against people in Berserk, particularly by those who serve the Holy See. The Count from the third major manga story uses the charge of heresy to get himself people to eat, being an Apostle. And Mozgus in particular is verymuch merciless in dealing with those who he considers heretics.
Arachne from Soul Eater is described as a "heretic Witch" because of the way she created the original magical Weapons features in the series, namely, by taking a normal human soul, a weapon, as well as the Soul of her fellow Witch (holding the power of transformation). Thus, she's hunted not just by the good guys but her fellow Witches.
Aleister Crowley was once one of the greatest sorcerers in the world, but then he decided to defect to the Science Side. Given that there is a secret Magic Versus Science war going on, he's become one of the most hated figures in the Magic Side.
Richard Brave is a sorcerer who wields a Flaming Sword called Lævateinn. The Magic Side declares him a heretic because the sword uses a combination of magic and science to work instead of pure magic. In response to the Magic Side dissing his finest creation, Richard declares his hatred of the Magic Side and tries to get revenge.
From the same author, there's recurring villain Martel in the Elenium, a former Church Knight who turned to the worship of the Dark God Azash and committed various atrocities since.
The Church in the Safehold series brands the entire nation of Charis as being heretics, mainly because they had the gall to survive the Church's attempts to obliterate them out of sheer paranoia. So far, despite having called down a holy war upon the Charisians, they have yet to learn that many of the leaders of Charis really are heretics, although the heresy they believe in (That the Archangels were not really divine messengers) is actually true.
The Preacher in Children of Dune certainly counts as this. He wanders the cities and settlements on the planet Arrakis, speaking out against the religion that has grown around the late Paul Atreides and his sister Alia. Of course it turns out that the Preacher actually is Paul, having walked blind into the desert several years before, thus essentially excommunicating himself from the dogmatic power structure that he had begun to hate.
The Damned One is the history's greatest heretic in Arcia Chronicles. The twist in his case is that he is actually St. Erasti, one of the most (if not the most) revered saints of The Church. This knowledge was so dangerous that The Churcherased all connections between St. Erasti and the Damned One from history after his defeat.
Oelita, the Gentle Heretic, in Courtship Rite, preaches against cannibalism and the belief that the moving light in the sky is a God. When our heroes are told of her by the clan leader, they assume they're going to be sent to kill her, and are shocked to learn that they're being ordered to marry her, and bring her congregation under Kaiel influence.
Lots of this in the Branion series, which features a divine royal family whose monarch is a God in Human Form, the Vessel of the Living Flame.
Book 1: A prince disobeys his mother, which given her status is heresy as well as treason.
Book 2: A Seer priest is part of a conspiracy to murder the Vessel, repents, and joins the Heir's protectors. The leader in charge of this Ragtag Bunch of Misfits follows an entirely different faith, and his own God has ordered him to protect the Flame's Vessel.
Book 3: The Vessels themselves are heretics, having converted to a different religion and trapping the Flame within their own bodies; the protagonists rescue It by seducing the Vessel, having his firstborn son and raising him to kill his father — also heresy, since this is like killing Jesus to free God from his human prison.
Book 4: The protagonists are a heretic cult, trying to give the other three Elemental Powers their own avatars.
The Imperium is just so big that the more realistic Ecclesiarchs have given up on ever achieving a uniform Imperial Cult, and must tolerate Him on Earth being worshiped according to different worlds' customs - Humanity's unifier made divine, a sun deity, the Omnissiah, the Allfather, etc. But at the same time, groups like Genestealer Cults, to say nothing of covens dedicated to the Dark Gods, are quite capable of masquerading as properly pious Imperial citizens until they're ready to sacrifice a planet to their dread masters. As a result, the Inquisition gets to spend a lot of time determining which religious groups fall within an acceptable level of deviance, and which need to be burned at the stake. As a rule, it errs on the side of caution.
The eponymous character from Heretic, of course. The Heretics in question were the Sidhe elves, the only race of beings not subject to the sorcerous mind control of the Serpent Riders, and thus targeted for extermination by their minions.
The Heretic Leader from Halo 2, an Elite who learned the truth about the "Great Journey" from 343 Guilty Spark and tried to warn the rest of the Covenant. The Arbiter is also branded a heretic at the beginning for his failure in the previous game, but that's really just an excuse to have him executed for his failure. He abandons his own religious beliefs after discovering the truth about the Covenant and ends up leading a splinter faction which allies with the "heathen" humans.
Ramza from Final Fantasy Tactics gets branded as a heretic when he runs afoul of their Ancient Conspiracy and kills a (demon-possessed) bishop in self defense. On the other hand, Olan Durai is also burned at stake for trying to reveal the truth behind The Lion War and Ramza's unsung heroism.
Billy from Xenogears rejects the doctrines of his church once he learns of its sponsorship and purpose.
Pellegri from Xenosaga stops just short of accusing her superior, Margulis, of heresy when he questions the authority of Lord Heinlein.
On that note, Shion and Jin, who both are likely to have extensive ties to the Ormus religion - physically beat the crap out of The Pope at the end of Episode II.
Yuna becomes a heretic in Final Fantasy X when she resolves to reject the teachings of Bevelle and fight Sin to destruction.
Happens to quite a few people in that game, notably the Crusaders being excommunicated for their use of machina, despite their perfectly good intentions and their continued belief in Yevon.
Not to mention the clergy actually backed the attempt to use machina to fight Sin. As soon as it failed, they pretended otherwise.
Nero rejects the teachings of his church to save his lover, Kyrie, in Devil May Cry 4.
In Medieval II Total War, regions where your faith isn't overwhelmingly dominant may spawn Heretics, or even convert a Priest you have stationed there to heresy. Since Heretics spread heresy and cause religious unrest, it's a good idea to have your Priests subject them to trials and burn them at the stake. If you're Catholic and you don't deal with Heretics, The Pope will send Inquisitors to your lands to start examining family members.
Byakuren Hijiri from Touhou is a heretic by the virtue of being compassionate to the Youkai. In this settings, the very presence of Celestial beings can harm Youkai regardless of either sides' morality.
Before that, there was Rikako Asakura, who was branded heretical for believing in science over magic.
In Mass Effect 2, it is revealed that the Geth the player had been fighting in Mass Effect 1 were actually a fanatical splinter group called Heretics by the True Geth. Making up about five percent of the total Geth population, Legion emphasises that the Heretics chose to worship the Reapers, instead of upholding the rather non-religious notion of self-determination of the True Geth.
In Crusader Kings 2, characters can adopt a variety of historical heresies. They tend to be loathed by anyone from the main religion, and imprisoned and forced to convert back. Unless a very powerful king adopts the heresy...
Before The Elder Scrolls V: Skyrim, the end of the Great War between the Empire of Tamriel and the Aldmeri Dominion saw the Dominion force the Empire to ban the worship of Talos, as the xenophobic and elven-supremacist Thalmor utterly refuse to recognize the ascension of a man into the ranks of the other Eight Divines. This has the effect of making all those who still worship Talos heretics in the eyes of the Thalmor, who arrest or summarily execute Talos worshipers they come across depending on their mood.