Divine Date

Zeus must have had some great pick-up lines.

A character is romantically or sexually involved with an actual god or demigod, like Zeus. Or even Satan! Hey, if you're Pals with Jesus, you can hook up with these folks pretty easily. The relationship may be short-term or long; the important thing is that it involves a deity. (If the character merely has powers like a god, that's more likely to be an example of Man of Steel, Woman of Kleenex.)

Particularly common in some mythologies where Everybody Has Lots of Sex—Greek Mythology is noted for this.

If the other partner is also a deity, you have an example of a God Couple; otherwise, it is presumably a form of Interspecies Romance. If the relationship leads to offspring, then you have Divine Parentage.

Compare and contrast Did You Just Romance Cthulhu?. May occur in the Magical Girlfriend genre. For the metaphorical version, where the deity may or may not exist and no actual romance or sex is involved, see Married to A God. Completely unrelated to Sex God. Usually.

Examples of Divine Date include:

Anime and Manga

Haruhi Suzumiya is forcefully romancing Kyon, who isn't quite sure who he wants.
Tenchi Muyo!
- Two of the three goddesses, Washuu and Tsunami, in the body of Sasami, are part of Tenchi's Unwanted Harem.
- Tokimi, the third goddess, ends up staying in his house in the very last episode (an extra episode to wrap up loose ends). It's up to interpretations if she joined the harem but given his track record, we can safely assume "yes."
- Considering Tenchi's status it's also arguably a God Couple
Ah! My Goddess features a Goddess as a Magical Girlfriend.
Sailor Moon is not quite a goddess, but she may as well be one in the Distant Finale, and not only does she have a token boyfriend who's always in some kind of peril, but her Five-Man Band is very devoted to her. (In the manga, Rei and Minako are shown talking about giving up ever having boyfriends because they'd rather be dedicated to protecting Usagi.)
In the Shoujo manga Akuma na Eros, the female lead Miu literally dates Satan.
The Mikos Words and The Witches Incantations
- Tsumugi is revealed to be so pure, she can only survive in continuous presence of a god, such as the one who resides in her shrine. So Letty goes out, badmouthes said god, and absorbs part of her divine essence, effectively becoming a demigod herself, just so that Tsumugi can travel with her. Yeah, she's way awesome.
- Speaking of the god, she adopts Tsumugi's form and takes over the shrine so the miko can stay with Letty. She also takes Tsumugi's hidden bodyguard as a servant and spends most of her time flirting with them. Since the bodyguard had a thing for Tsumugi, this leaves her... flustered (Though apparently not unhappy).

Comic Books

In the spin-off of Johnny the Homicidal Maniac, Squee, Squee's classmate is the son of Satan. His mother didn't realize that until years into their marriage, and comments on how it's ironic as she's "always been a good Christian woman."
Being that any number of gods from classical myth are regular players in any number of comic titles, this is a relatively common occurrence. In The Avengers, for example, Hercules is often portrayed with various lovely young women.
- Loki is much like his mythological counterpart; in one story, Spider-Man is surprised to discover Loki has a daughter; Loki replies, "I have hundreds. I'm a Norse god, it... happens." Fortunately, he is not the deadbeat dad type.
In The Sandman the eponymous character has his occasional romances with mortals. They don't seem to end well.
In Lucifer, Mazikeen (whose divinity is as ambiguous as a lot of the entities in the setting) maintained a relationship with the human woman Beatrice.
- She belongs in the Lilim who aren't demons, angels, humans or gods, but something in between all four.
The Incredible Hercules:
- Herc manages to bed quite a few mortals, in addition to at least one other deity. Further expanded in Agents of Atlas, when Namora (one of the mortals previously noted) and Siren spend several days travelling the globe meeting with Herc's various mortal, non-super paramours after Herc's demise.
- Of course, at various points in Hercules' publication in various Marvel books, his father Zeus (as noted in the Mythology section below) is also noted (and observed) as continuing his mortal-chasing ways (he insists that his busty new secretary simply makes the best lattes). The phrase "mortal fever" was bandied about.
Wonder Woman: Cassie Sandsmark, the second Wonder Girl (or third, depending on how one counts these things), was the daughter of Zeus and mortal archaeologist Dr. Helena Sandsmark.

Film

When asked if she was a devil worshiper, Elvira allegedly replied "I dated him once".
Narrowly averted in The Adventures of Baron Munchausen. The Baron and Venus engage in some serious flirting, but her husband manages to keep it from going too far.

Literature

Discworld has a relationship between Susan and the Anthropomorphic Personification of Time, although Susan is one quarter anthropomorphic personification by adoption herself. Said anthropic personification of Time is also the son of a different anthropic personification of Time with a human man.
- She also had a brief fling with a former angel of Rock and Roll.
The parents of pretty much all the main characters in Percy Jackson and The Olympians are Greek gods, except Grover and Rachel Elizabeth Dare. And its successor, The Heroes of Olympus. But this one mixes in the Roman pantheon of aspects as well.
In The Redemption of Althalus, Althalus lives, loves, and has a child with Dweia. Dweia just happens to be that universe's mother goddess.
The Inheritance Trilogy has plenty of examples from Yeine/Nahadot and Oree/Shiny aka Itempas to various other mentions of humans, gods and godlings all dating/having sex with each other.
Gardner F. Fox's Niall Of The Far Travels stories. Niall (a Conan-style barbarian) has Emalkartha, goddess of the Eleven Hells as his girlfriend.
In Tamora Pierce's Immortals series, Daine's mother Sarra turns out to have had a god for a lover. He cares for her so much that after her death he petitions (succesfully) to have her made a goddess as well.
In the Garrett P.I. novel, Petty Pewter Gods, Garrett ends up being seduced by a few, including a love goddess named Star and a couple of minor godlets who can take the forms of owls.
In The Silmarillion, the Elf Elwë marries a minor goddess, Melian. Their daughter, Lúthien, is an Elf of unusual beauty and magic power.
A major subplot in Warbreaker involves Siri's Arranged Marriage to God-King Susebron, who is revered as a literal Physical God by his followers. Though Susebron is initially presented as a tyrant, he turns out to be a Puppet King and quite friendly, if naive, and he and Siri end up actually falling in love.
In The Age of Five trilogy, the god Chaia is said to have had many relationships with humans, driving some of them mad when he left them because he was capable of giving them pleasure of such unbelievable heights that afterwards they were unaffected by any other pleasure reality could offer. The main character, Auraya, has a relationship with Chaia, although ultimately never loves him and ends up breaking it off.
At the beginning of the Books of Swords, Mala has anonymous sex with the Emperor, who turns out to be G-d. Yambu had had a long-term relationship with him, although they'd been separated for many years by the time the series began. They do finally get married at the end of Shieldbreaker's Story.
Any mortal dating an Incarnation could count.

Live-Action TV

Russell T. Davies's The Second Coming ends on a date between Judith, a normal human woman, and her life-long friend Steven Baxter, a bloke who just happened to discover he was the son of God. She ends up killing him.
Becky, the fangirl expy, from Supernatural was dating Chuck for a while, who, as it turns out, was actually God.

Oral Tradition, Folklore, Myths and Legends

Zeus in particular seemed to want to bone anything with boobs and a vagina.
- You're crediting Zeus with too much discernment.
- Aphrodite was fairly notorious in this regard as well, as one might expect from a Goddess of Love (and Sexuality). It wasn't just the girls who got the benefit of divine company.

Tabletop Games

In Dungeons and Dragons various characters date with deities, most notably Elminster. For example, in the Forgotten Realms setting Elminster the Sage once had a romantic relationship with Mystra, the goddess of magic.
- Also, Eilistraee is a goddess who encourages dancing and revelry, and if a worshiper remains loyal to her cause long enough, she might show up in person at one of their moonlight rituals and offer to have the next dance, truly a once-in-a-lifetime experience.
Gods are unusually accessible in the world of Exalted, so this is a fairly common trope. Even more so if you count the titular Exalted, who start off human but are endowed with more than enough power to match and even surpass any god.

Video Games

Disgaea 2: Cursed Memories:
- Adell is quite cozy with Demon Overlord Rozalin, known in her previous life as "the God of All Overlords". But then, this is a Nippon Ichi game...
- In the first Disgaea, Laharl's human mother married an overlord.
La Pucelle Tactics
- It ends with Priere and Croix, i.e. the Dark Prince as a couple.
- Priere managed to match him later on though when she became the overlord of the local Netherworld.
Many of the endings in Soul Nomad also qualify as Revya is a World Eater (race of beings of god like power, some of which are gods themselves). May also count for the female ending with Gig.
It is possible in Neverwinter Nights Hordes of the Underdark to end the game as ruler of the eighth layer of Baator with power falling just short of being an actual god, and remain in a committed relationship with any of the three love interests after the close of the game.
Eversion has a variation and major subversion in the good ending, you become an a Eldritch Abomination just so you can act out this trope.
In Romancing SaGa: Minstrel Song, the dancer Barbara catches the eye of The Minstrel, who is eventually revealed to be Elore, lord of the gods.
Harvest Moon: Animal Parade allows the male and female main characters to date the Harvest Goddess or Harvest King, respectively.
Prior to a patch that fixed it, in The Sims 3 you could totally woohoo with the Grim Reaper and have his awesome, pitch-black babies.
May have occurred with The Curse of Monkey Island's Voodoo Lady. When asked about the god Quetzecoatyl she describes him as a "really nice guy, not that bloodthirsty at all. Shorter than you might think."
In Tales of Innocence all party members and many other characters are the human reincarnations of the game world's gods, though this being a JRPG they generally shy away from admitting to relationships. A better example is the Grigori tribe are blood decendants of one of said gods, resulting from a god's relationship with a mortal, and repeated interactions with the tribe every few generations to keep the divine bloodline strong.
The Legend of Zelda Skyward Sword: It's quite possible Link ends up regularly dating a deity in mortal form after the ending of almost any game! But at least Zelda doesn't seem to know in most of those lifetimes that she is the Queen of Lesser Gods, Hylia, in mortal form...
Lunar: Alex and Luna, in the first game. Hiro and Lucia, in the second.
In the dating sim HuniePop, once the player dates and beds all eight of the main (human) cast and Kyu, the final "challenge" is Venus herself. Seeing as this is the equivalent of a Final Boss, it's not easy; Venus is the actual Goddess of Love, and very little can impress her.

Theatre

One Touch of Venus is about the actual goddess Venus being in love with a barber from suburban New York.

Web Comics

Andy of Casey and Andy, who's been dating Satan from around strip 50 to the current (and final) strip, 666.
In Gunnerkrigg Court, Matt had a Meet Cute with the Chinese moon goddess Chang'e. Then she walked off with his jacket and his mp3 player. Women, huh...?

Western Animation

On South Park Satan had an abusive relationship with Saddam Hussein, Satan being the abused. Satan later hooked up with a Nice Guy named Chris, before deciding to just be with himself for a while. He later hooks up with one of his minions, which also doesn't work out.
Courage the Cowardly Dog parodies this with the Greek-mythology-inspired "Goose God" (Exactly What It Says on the Tin) trying to woo Muriel.
Gargoyles had an episode set in Ireland where a man is unwittingly dating the banshee. Though he later discovers he's a magical being as well, a hero destined to banish the banshee from Ireland. And Word of God states that if the series had continued the two would have fallen in love for real.