Semi-Divine

A character that's not a fully supernatural being (such as a god, angel, demon, spirit in general, abomination, etc.), but has a touch of it or more in them. The character may be the offspring/descendant of supernatural creatures and mortals, or is part of a race that's inherently part-supernatural or in between. For that matter, the character might have even become part-supernatural as a boon from the Powers That Be or their own personal attempt to Ascend to a Higher Plane of Existence. The reverse can also happen, as a fully supernatural being Descends from a Higher Plane of Existence and winds up with a "mere" fraction of their former supernatural touch.

These characters tend to exhibit several Stock Super Powers, and if they aren't outright Immortal, they're almost guaranteed to be Long Lived. They may or may not qualify as Humanoid Abominations (who themselves have a high chance of being this character type), and that's if they look humanoid in the first place.

The Antichrist is almost always an example. Changelings are also frequently found to be some mix of human and faerie. Divine Parentage, being Touched by Vorlons and a Deal with the Devil are common origins for this type of character. Having a piece of a magical being in you may also count.

One can think of these characters as beings that are partly Made of Magic (or spirit-like beings in general).

As can be derived from the title, part-divine characters are one of the (if not, the) most common examples, which is unsurprising, considering the fact that many gods in mythology have had rather promiscuous lifestyles, and this would naturally extend to modern-day fiction. It should be noted, however, that this trope applies to any mix or midway between "normal" and purely supernatural beings, so this isn't limited to the literal Semi-Divine.

Anime and Manga

 * All of the Claymores are half-human and half-youma . They're born human and become half-youma by taking youma flesh into their bodies. A fallen Claymore warrior is called an "Awakened One" and is far more powerful than a pure-blooded youma.
 * Ichigo Kurosaki of Bleach. His mother was, as far as we know, a normal human. His father is a retired Soul Reaper, meaning that he's basically a human/ghost hybrid.

Comic Books

 * Captain Marvel: "I'm not a man ... I'm not a god ... but you, Billy: you're both."
 * Jesse Custer in Garth Ennis' Preacher (Comic Book) series, who is Blessed with Suck by literally having the "Word of God." (No relation to the trope of the same name.)
 * The Spectre qualifies, as he's a dead human who is the host of (the angel that represents) God's Wrath/Vengeance.

Literature

 * The White Court in The Dresden Files. Their souls are half demon due to a demonic symbiote that gives them superhuman abilities and incredibly good looks, but at the cost of a Hunger for human emotions. The Raith family is particularly noted to go after lust.
 * Daine in Tamora Pierce's Wild Magic series is the daughter of a minor god (of the hunt) and a mortal woman (who becomes a minor goddess when she dies).
 * There's also the Old Kingdom books by Garth Nix. The world was created by  spirits of Free Magic, but in order to protect the world and humanity, the Seven created the Charter and bound most of the Free Magic in the world. Four of them poured most of their power into mortal bloodlines; the Clayr, the Abhorsen, the royal family and the Wallmakers. Consequently, although not directly related to a deity, they all do have powers inherited from a god (or close enough).
 * The Kushiel's Legacy series establishes that the D'Angeline people are like this; descended from God's son and his angelic companions.
 * Vishous from Black Dagger Brotherhood is another example; he is the son of the Scribe Virgin, the deity vampires pray to in his universe. He also has a twin sister named Payne....
 * In the Percy Jackson book series, most of the main characters (at least the children) are demigods, born of a god and a human.
 * And the sequel to the series, The Heroes of Olympus, does the same. Most of the main characters are the children on the Roman gods now, however.
 * The Delphaes in the The Shining Ones started as humans but now are slowly evolving into gods. As a result, they possess awesome powers, but they can also melt alive anyone who gets too close to them.
 * In the Inheritance Trilogy, demons are the descendants of both god and mortal, and include
 * The Lord Ruler of Mistborn presents himself as a Physical God . Word of God calls people like this from across the overall cosmology of Sanderson's works "Slivers".

Live Action TV

 * The vampires of Buffy the Vampire Slayer. They retain their (enhanced) bodies and their minds, but their formerly human soul is replaced with that of a demon.
 * Hell, most of the "demons" are an example. They're the product of countless generations of interbreeding between humans and true demons, who were more like Eldritch Abominations than their typical depictions.
 * An example of a mortal attaining semi-divine status happens in Angel. Cordelia was dying because her psychic visions were causing Power Degeneration. After refusing a divine offer to give up her powers and live a normal life in order to continue doing good, she was rewarded by being turned part demon. Being allied with the (generally) good Powers That Be, her demonhood had no cosmetic effects, gave her immunity to Power Degeneration, and healing abilities.
 * Also from Angel, the fifth season gives us Ilyria, an Old One, a pure demon. Her current shell is too weak to contain her power, so Team Angel siphons off some of her power. So now she's a semi-human Old One with a fraction of her former strength.
 * during the fifth season of Supernatural..
 * Sam and the rest of the psychic children. Their powers originated from.
 * In the Stargate Verse, any character on the path to ascension displays a plethora of Psychic Powers, which signifies how close they are to becoming the god-like ascended.

Music

 * Leontius from Sound Horizon's Moira is noted to be descended from the Thunder God from his mother's side..

Mythology and Religion

 * The original demigod, Gilgamesh himself, was actually two-thirds god.
 * Dragons in eastern mythology are often part-godly in nature.
 * Classical Mythology had a ton of them:
 * Heracles: The son of Zeus and Alcmene.
 * The swan sisters, Helen and Klytemnestra and their twin brothers Castor and Pollux: children of Zeus and Leda.
 * Odysseus spent a few years on an island shacked up with a minor goddess. The Odyssey doesn't mention any children, but there's no such thing as a divinity that isn't Super Fertile. Later myths explore the lives of their many, many, many children.
 * Frankly, Zeus and a few other gods deserve a special folder all their own. Those rapists were all up ins. And gods make babies. Always.
 * Aeneas's mother was Aphrodite. Dude founded Rome.
 * There were whole races that were thought to be somewhere between the Olympians and mortals in terms of divinity, such as the nymphs.
 * Jesus Christ, although in some denominations, he is both 100% divine and 100% human.
 * The Nephilim of Judeo-Christian mythology are thought to be the children of angels.
 * Merlin is thought to be the child of a demon and mortal, although in the original myths he was depicted as something of a fey spirit, so half-fairy was more likely.
 * In Hindu Mythology, Ganesh was a boy who was appointed by the Goddess Parvati to stop anyone from entering her bathroom while taking her bath. When Ganesh stopped her Husband Shiva from entering, Shiva cut his head off. After Parvati found out what happened, she became angry, and Shiva had to fix Ganesh by attaching an elephant's head to Ganesh. Ganesh was given demigod status in the Hindu pantheon, and is supposed to be a sort of door god.

Newspaper Comics

 * Phil, Prince of Insufficient Light in Dilbert.

Tabletop Games

 * The eponymous Exalted are mortals that are blessed as the divine champions of the most powerful gods and god-like beings in the setting. As a consequence, they tend to have abilities that far exceed those of the "normal" gods and spirits, which is most obviously seen in the Solars and their derivatives.
 * It's worth pointing out that most Exalted become what they are when a normal human's body and soul are combined/merged with a shard of literal divine power.
 * The Scions are the children of gods, and can ascend to godhood themselves.
 * In Dungeons & Dragons
 * Tieflings and Aasimar are descendants of fiends and celestials, respectively. And the "Planetouched" in general, as they're all descended from something not of mortal worlds. This may dilute down to "some sort of magical bloodline".
 * Every sorcerer gets their powers from some kind of encounter with a magical force somewhere back in the family tree (either directly or indirectly.) Some of them are divine, infernal, or even draconic.
 * Planescape introduces proxies, champions of deities invested with divine power and will -- whether formerly mere mortals, petitioners (common dead folk) or otherwise. This status can be recalled by the issuing deity, however. The long-term ones are often transformed into whatever creatures serve their boss. They are those who get sent for really important errants or left to guard the deity's home when the boss is absent.
 * Quasipowers, in D&D3+ designated as Divine Rank 0 entities (normal beings have no rank at all). Such an entity isn't a god for most purposes (they don't grant spells, get to be present in several places at once by spawning avatars, etc), but they have many of the mechanical benefits of being considered divine (immortality, max HP, a good degree of Nigh Invulnerability). Usually they are either autonomous special assistants of the gods raised above "common" fiends/celestials/whatever by their respective high-ups (e.g. the Valkyries) or wannabe/fledgeling deities (e.g. those Lords of the layers in Abyss who aren't already full deities).
 * Forgotten Realms has the Chosen of Mystra. They were intended as the only ones of their type, to both divide and safeguard her power by stashing some of it away. However, this led to creation of copycats by the authors who didn't ask.
 * Ubtao (the Great God on Chult, whose favoured beasts are dinosaurs) makes Bara - mortal humans granted a single power on godlike level and immortality (or at least immunity to aging). They are supposed to protect his other followers, since the place is rather dangerous at better times, at worse times even all those dinosaurs stomping around are not the greatest threat, and Ubtao tend to take long naps.
 * The Primarchs and, to a lesser extent, the Space Marines of Warhammer 40,000. The Primarchs are the 20 "sons" (or rather gene-tweaked clone babies) of God-Emperor, and while they aren't as powerful as him, they're nigh-godly unto themselves. The Space Marines are warriors that are Bio Augmented with the geneseed implants created in turn from genetic material of the Primarchs, and they're basically an army of individuals who can each slaughter a thousand men by themselves.
 * Anyone with Outsider Taint in Cthulhu Tech.

Video Games

 * The Demonspawn and Demigods of Dungeon Crawl. They can be created through magical experiments, breeding with demons and gods/angels, (un)holy pacts, or any number of other ways. The former are very versatile and have a wide range of (random, but usually powerful) abilities from their demonic mutations, but are weak against evil-smiting powers. The later have the highest base attributes in the game, and have a lot of HP and mana pools, but they level slowly and can't worship a god, which is pretty bad, as a lot of powers and bonuses can only be gained through religion.
 * In the Baldur's Gate series, the Bhaalspawn are the children of Bhaal, the Lord of Murder. He sired them so they would kill each other until none remained, at which point his essence that was scattered among them would have accumulated, and his chosen follower, Amelyssan, would have performed rituals that would have brought him back. Neither Amelyssan nor the last Bhaalspawn (the protagonist) complied to these plans, however.
 * In fact, Amelyssan was something like 99% god by the end of the Throne of Bhaal expansion. After defeating her, the PC (him/her)self ascends to full godhood.
 * Dante and Vergil of Devil May Cry. They're both the sons of Sparda, a demon who made other demons look like wet tissue paper in comparison.
 * In F.E.A.R, the unnamed child that was produced by certainly counts. It's even described as a ghost in the flesh.
 * In Disgaea, Laharal is the son of the former overlord and a human.
 * The Dragonborn of Skyrim, who was been born with the soul and blood of a dragon (who are otherwise known as aedric spirits), but has the body of a mortal.

Visual Novels

 * Divinity in Fate Stay Night is somewhat arbitrary and is ranked; the closer you are to the gods, the higher the rank. This results in heroes such as Gilgamesh, who is two-thirds divine (Rank A), but has his divinity reduced to Rank B since he himself dislikes the gods, and Medusa, who has had her divinity reduced severely after being transformed into a demonic creature.

Web Comics

 * Gunnerkrigg Court has, who's part fire-elemental. Also, Brinnie comes close from the other end — a Valkyrie who was a schoolgirl at the Court for a while, though still capable of opening portals in the air.

Web Original

 * The hero and his siblings in this Newgrounds Flash animation.
 * in Tasakeru.

Western Animation

 * Genie in the Aladdin sequels and series. After being freed, he has gone from having "phenomenal cosmic powers" to "semi-phenomenal nearly-cosmic powers".
 * Danny Phantom, along with Vlad Masters and Danielle Phantom, are half ghost, though there was no breeding between ghosts and humans involved: the former two were both results of lab accidents, and the latter was cloned.