In many versions of the Arthurian mythos, Morgause is Arthur's half-sister. Their son and nephew, Mordred, eventually destroys Arthur's kingdom.
The Questing Beast was said to be born from a princess who lusted after her brother, and slept with a demon who promised to make him love her back. Instead the demon made her hate her brother, and when she became pregnant she accused him of raping her, prompting her father to execute him. Before he died the prince said that if he was innocent, it would be proved by his sister giving birth to a monster.
In Norse Mythology (at least according to Heimskringla), marriage and breeding between brother and sister were common amongst the Vanir before their alliance with the Aesir. The twins Freyja and Freyr were children of Njord with his unnamed sister. Loki in the Poetic Edda also once accused Freyja and Freyr of sleeping with each other, though it's not clear whether this is more than slander.
Through in the following stanza Njord defends Freyja, but it's for the infidelity-claim. The incest part is not mentioned. It does make you wonder through...
In the myth of creation according to the Aztecs, Quetzalcóatl was a celibate god. Then he got drunk after a fight with his brother/alter ego Tezcatlipoca and had sex with his sister.
In fact, almost by necessity most creation myths involve this, particularly among gods and titans like Zeus and Hera, and their grandparents Oranos and Gaia — who were mother and son too, technically.
There was also a myth about Poseidon's short affair with Demeter (his sister) which may or may not have been consentual. (Whether it was seduction or rape was unclear, something that is often the case in these myths.)
The whole pantheon is filled with incest of just about every conceivable combination. Brother-Sister Incest is probably the least strange of it.
Heracles is a textbook case. His father Zeus was a son of Kronos and Rhea, who were brother and sister (children of Gaia and Oranos). His mother Alcmene is also Zeus' great-granddaughter (through her grandfather Perseus, son of Zeus and Danae). When he ascended to Olympus, Heracles got to marry his half-sister and great-aunt Hebe, daughter of Zeus and Hera, Zeus' sister and wife.
Classical Mythology also had Byblis falls in love with her brother Caunus, and defends their relationship by pointing out how many immortals have had incestuous relationships. Their story was later retold by Ovid.
According to the Odyssey, Aeolus, Keeper of the Winds, married his six sons to his six daughters.
In another story, incompatible with the above, Aeolus' children Macareus and Canace had a secret affair. When Canace gave birth to a son, their ralationship was revealed. Aeolus exposed the child, sentenced Canace to death and Macareus killed himself.
Averted in the Rigveda. Twins Yami and Yama are the first created mortals, and Yami attempts to seduce Yama so they may continue the human race. Yama refuses on the grounds that she's his sister so that's just wrong.
In ancient Hawaiian myth, the divine couple who gave birth to the Hawaiian islands were either siblings or half-siblings. They also had a daughter who grew up to be so beautiful that her father begun a relationship with her and fathered two more kids. This became the basis for a practice known as pi'o, intentional incestuous mating amongst the ruling class. Extensive genealogies were kept in order to produce the most inbred (and thus, godly) chiefs possible. The commoners were forbidden to do this out of fears that they would start producing children with chieflike levels of mana.
Alchemy has many incest symbols, especially the hierosgamos or coniunctio ("sacred marriage" or "union"), a chemical wedding of male and female, brother and sister. The rebus is often shown as an incestuous brother and sister, portrayed as a union of Sol and Luna, sun and moon.
Egyptian Mythology: Isis and Osiris, Nephthys and Set. In some versions of the mythos, Isis gives birth to reincarnations of herself and her husband who mate even before birth - may sound icky at first, but this is in all probability a fertility myth inspired by the constant rebirth of plants and harvest.
Nut and Geb are also technically siblings and in love with each other, but are forced to remain separate to maintain the order of the cosmos.
Chinese Mythology is unclear as to whether human beings originated from divine incest: The first god Fu Xi and the first goddess Nu Wa, both of them beings with human torsos and snake tails, are at once brother and sister as well as husband and wife. It is usually stated that the first human are created as clay figurines by Nu Wa, but both deities are credited as the creators of human.
Japanese Mythology have the first deities Izanami and Izanagi. Some versions of the myth also have the sun goddess Amaterasu married to her brother Tsukuyomi.
Adam and Eve. Since humanity is still young and vital, it's a case of Incest Is Relative until more careful selection is possible or even necessary.
Eve was made from Adam's rib, so unless God worked some additional magic, they were brother/sister in a cloning sense.
Adam's and Eve's children by the more literal readings could only have had other family members to mate with but its never said explicitly. Cain's wife who is arguably the 5th human mentioned but comes from nowhere. After Cain killed Abel, he went into exile away from his family, but he went on to marry the unnamed lady. The fifth chapter states Adam and Eve had other sons and daughters, so she could've been one of them. Alternatively, some think the implication is that there were other people created other than Adam and Eve, and they were just the first.
The punitive Great Flood leaves only four married couples alive — three of the men are brothers, and the fourth couple are their parents. The following children would have no one to marry but their cousins or siblings. As Genesis also claims that people lived an average of 400 years back in those days, the much shorter lifespans following the Flood can be taken as a result of that tragically narrowed gene pool. This is all consistent with the Bible's theme of various cataclysms as a consequence of man's pride leading to repeated falls.
Not only for humans. Aside from bringing seven pairs of a few species designated acceptable for sacrifice (and any domesticated animals the family might have had), the Biblical account puts "every air-breathing animal on the planet" through the same genetic bottleneck.
Sarah was Abraham's half-sister, as well as his wife. So when he told the Egyptians "she is my sister" he was telling a half-truth... that caused all sorts of mayhem. The Pharaoh at the time had this lovely 65-year-old taken to his house, and the Pharaoh and his house were subsequently stricken with great plagues. Upon learning that Abram had not told him the important fact that she was his wife, he told Abram off and sent them away. Fast forward twenty-five years, and they went down to Gerar, still planning the same omission. Abimelech took her, and learned from a vision that she was Abraham's wife, and that Abimelech would die if he didn't give her back. He did, but asked Abraham what could have possessed him to omit such an important detail. He explained his reasoning, but also that she was, in fact, his sister from another mother, but from the same father. He let them live there and gave them stuff, and Abraham prayed and the wombs of Abimelech's house were reopened from being stopped up.
King David's oldest son, Amnon, lusted after his virgin half (?) sister, Tamar, so badly that he pretended to be ill so that Tamar would come to his room to feed him. He then raped her over all of her protests (and it being a gigantic no-no in Jewish law). Their other brother Absalom didn't take it kindly. Some try to argue they were Not Blood Siblings. The interesting part is where she pleads with him to talk to their father about it with the assumption that David would approve the marriage. Now it's very possible that she was just trying to put him off but it can be assumed that she wouldn't have made the plea if it was completely implausible. Maybe the taboo of being an unmarried, deflowered woman was a greater stigma than being married to a half-brother.
Other than the story of Amnon and Tamar, however, all of these incidents took place before the books of Leviticus and Deuteronomy, which specifically outlawed these practices, were written. The very word "incest" is a term that has been retro-actively applied, coming as it does from Latin, the language of ancient (yet still much younger than Israel) Rome. Though there are indications that the Law was already known to some extent before Moses wrote it down (e.g., Noah knew which animals were clean before Leviticus 11 was written).
In Zoroastrianism there is a concept known as xwēdōdah, or the holy union of father and daughter/mother and son/brother and sister. It was and still is considered by the religion as the most pious acts one can perform as a Zoroastrian for reasons that are far too complicated to explain in a simple entry. However, since nothng in the religion requires it and most people simply don't want to marry someone in their family, it very rarely happened outside of royalty.
The Pearl Of Great Price one of the four standard works is LDS (Mormon) canon and scripture says that the sons and daughters of Adam and Eve began to "divide two and two in the land ... and they also begat sons and daughters" meaning it's explicitly Mormon doctrine that everyone is a product of sibling incest. While this neatly explains where Cain's wife came from (she was a sister) it... brings up other issues.