So you are a freak of nature, a witch, a Super Hero, or a Chosen One. You are loaded with supernatural powers, and between going to work or school you have some world saving duties to attend to that need to be kept secret. And on top of that, you also need to balance it out with a love life!
But you can't tell your boyfriend about it! He'd freak out and leave you, or worse. But then, you can't keep it a secret forever, either. At some point, one of your supernatural incidents will inevitably happen exactly when you were having a romantic dinner. Or maybe your relationship has simply reached the next level, and you feel that you need to be completely honest with him.
So what now? How will he react? Well, it turns out he's perfectly okay with it (well, for the most part) and completely understands. That's right, as a reward for your sacrifices, the Powers That Be will make sure that you end up with a truly noble and loving soul who loves you for who you are and doesn't care what you are. So no worries!
This trope is a Double Standard, in that wives and girlfriends are pretty much automatically accepting of their Action Hero husband/boyfriend's actions, whereas the number of husbands/boyfriends who automatically accept that their significant other is an Action Girl are pretty thin on the ground. For the guy who is a super and needs a girlfriend, his powers are often a plus for her because it makes him more amazing. For women, finding a guy who truly doesn't have a problem with dating someone with superpowers when he's a Muggle is the bigger issue, because, well, No Guy Wants an Amazon.
Compare Freakiness Shame, when a disguise forms part of the powers. Compare to Violently Protective Girlfriend for the Action Girlvariant. Compare and contrast Non-human Lover Reveal, for the guy/girl who is on the other end of this trope. See also The Masquerade Will Kill Your Dating Life, which is an aversion of this trope.
Keiko Asakura from Shaman King had been dumped by every single boyfriend she had when they learned she was able to see spirits. Until the last Jerk Ass left her and a penniless musician with similar abilities comforted her. That guy was Mikihisa, and she would marry him.
Shuuji in Saikano. His girlfriend is a WMD? That's OK, things will work out. Actually, they don't.
Kenta Usui from Karin, except for the boyfriend part. Until the end, that is. Comes with him doubling as Karin's crush and the Marker's Secret Keeper.
In Awkward Silence Toono Satoru's boyfriend is the only one who can read his seemingly blank and expressionless face (other than an old childhood friend of his who doesn't show up until later volumes) and understand his emotions.
This is also central to the plot of Kotoura-san. Haruka Kotoura was friendless, socially stigmatized and severely traumatized due to her telepathic powers, and by the time she would actually drive people away. Manabe successfully broke her shell and became protective of her; and by this way she gradually became more like what she actually is—a conventional moe heroine. The only issue is, he is a pervert and still couldn't really control his sexual fantasies—except those fantasies were all directed to her, rather than other.
In Demashita! Powerpuff Girls Z, Souichirou eventually finds out in episode 45 that his girlfriend, Sakurako, transforms into Sedusa whenever she's jealous or has doubts about her relationship with Souichirou. In a rather d'aww-worthy moment, Souichirou's reaction is to shout at Sedusa that he doesn't care, he loves Sedusa and Sakurako...because Sedusa is Sakurako!
The majority of the Ashikabi in Sekirei are perfectly accepting of their Human AlienMagical Girlfriends. Minato in particular takes things in stride, and actively seeks any way he can help the girls out, whether it's providing emotional support, doing the laundry, or acting as the strategist.
Back in the Golden Age, Steve Trevor was this for Wonder Woman (a remarkably progressive move for the times), and not at all threatened by the idea of getting rescued by or mooning over a woman who was twenty times stronger than him. The Silver and Bronze Age characterizations of him were...unfortunatelyless so, which probably led to the relationship being deleted from continuity Post-Crisis.
Relax is an extremely heartwarming example. Why? Because the couple, Haye and Klee, initially met when the former bought her services as a prostitute. Not only is Haye completely cool with his girlfriend's occupation, but he also pays her just like any other client, despite the fact that she'd definitely do it with him for free.
Ultimate Spider-Woman: Change With The Light plays it straight to an extent. When Mary Jane Watson's boyfriend Randy Robertson finds out that she's secretly a web-slinging superheroine, he's not so much upset by the fact that she's a superhero as the fact that she originally wouldn't tell him the truth about it. What really pisses him off, though, is when he learns that her Arch-Enemy Jack O' Lantern knows her real identity.
In the Rise of the Guardians fic Guardian of Light, the main character Helen discovers that Pitch is her father. Jack isn't her boyfriend at this point, but he doesn't hold this against her despite everything, and is willing to protect her at all costs.
Elend in Brandon Sanderson's Mistborn. At least until he gets superpowers himself.
Seth in Wicked Lovely. When Aislinn tells him that she can see faeries, he has exactly one moment of "Is this a joke?" before accepting it and trying to help her with her faery situation.
In Discworld, Carrot is completely understanding about his werewolf girlfriend Angua, even the part about her not being human for one week out of four. She's actually upset that he's not upset about this at one point.
That was almost...almost one of the annoying things about him. She suspected he wouldn't mind if she shaved her head, or grew a beard. It wasn't that he wouldn't notice, he just wouldn't mind, and for some reason that was very aggravating.
In Parties and Potions by Sarah Mlynowski, Rachel is a witch and has to tell her human boyfriend Raf. It mainly escalates when she starts doing training for her witch "debutante ball" and ends up being gone whenever he wants to hangout with her. He is okay with it when he finds out, though.
Both subverted and played straight in Bewitched. The original Darrin (Dick York) was less than understanding, to the point of being downright hostile to Samantha when she used her magic. The Other Darrin (Dick Sargeant), on the other hand, tried his hardest to be understanding, the point that it was more the fault of Endora and the rest of Samantha's family that The Other Darrin didn't get along with witches.
Played with in the Sabrina the Teenage Witch TV series. Harvey does leave Sabrina when he finds out she's a witch, not out of intolerance but because she'd been using magic to mess with his life for years. He eventually does come back to her, though, and says he never had a problem with her being a witch per se.
Unless she's dating one of the undead, Buffy never got this on Buffy the Vampire Slayer. (Even Riley, who was himself a demon fighting super-soldier, had an inferiority complex due to dating a genuine superhero.) It's Willow who hit the boyfriend jackpot with Oz; upon being told the truth about the supernatural world she runs in, he replies, "Actually, it explains a lot," and just goes with the flow from there. Of course, Oz discovers he is a werewolf shortly after they begin dating, so he's more or less stuck in the supernatural world regardless, and Willow ends up having to play Understanding Girlfriend just as often.
Allison's husband Joe on Medium believes in her powers and is understanding and accepting of them.
In Merlin, 2x09. Merlin discovers Freya turns into a bastet at night, but he isn't afraid and still takes care of her. He even pets her cat's head...
In the TV version of Wonder Woman, played by Lynda Carter, esp in the first season (set in WWII), Steve Trevor comes across as completely comfortable with the fact that Diana is more physically powerful than he is, and in fact manages to work with her and make himself actively useful while giving every impression of appreciating her for who and what she is...and doesn't come across as unbelievable or weak, either.
In the TV version of The Tick, Captain Liberty and another female superhero discuss the difficulties of finding a boyfriend while picking up their dry-cleaning. Seriously subverted in this episode.
Roswell had Isobel and Jesse; she tries to send him away after he discovers she's an alien, but in the novel 'season 4', they end up together anyway.
This was a recurring problem for the ladies on Charmed, whose human love interests would either freak out at the idea of magic existing, or would end up six feet under very soon after learning and accepting the truth. Piper marries a Whitelighter, Leo (but after he eventually loses his powers, he becomes this), Phoebe marries a Cupid, while Paige's husband, Henry (a 100% normal cop) plays this straight, his only reaction to her confession being mild surprise.
This was also played straight by Grams' first husband before he died, but averted by every one after that. The girls' father, Victor, also seemed quite accepting (and is of the girls' magic in the present day), but it's implied Grams drove him away.
In Final Fantasy XIII, Serah wanders into some ruins and is made a Pulse l'Cie. Public opinion of Pulse l'Cie being... rather low, she tries to break up with Snow so he won't be associated with her should she be found out. He refuses to accept this, demands an explanation, and upon being told the truth says he will do anything to help her and proposes a few days later.
In Dragon Age II a non-mage Hawke can be this if romancing Anders or Merrill. Particularly if the player character is on the friendship path.
At Pandoras Tower Until I Return To Your Side, Aeron discovers his girlfriend Elena is cursed and will transform into a monster if not cured. Even with his his girlfriend in a half demonic state, he throws away his old life and start exploring dangerous towers, just to kill monsters and feed Elena with their flesh to reset the curse timer and try to cure her (and give her gifts when he can). You could say Elena is a really lucky girl.
A major part of several romances in the Mass Effect series, especially with the non-humans, is Shepard being this about their various issues. Aside from the inherent problems of romancing, say, a drell or a quarian, the strongest is probably Jack, who only really warms up to Shepard when she realizes he cares despite, not because of, her history and nature — that is to say, he truly loves her rather than pitying her. Of course, given the people Shepard is willing to let into the Ragtag Bunch of Misfits ("Asari? Krogan? TURIANS!?") it's only to be expected.
Also featured with the romance between Female Shepard and Garrus Vakarian, particularly in ME3. No matter what Shepard's done, such as bringing on the destruction of the quarian race or sabotaging the genophage cure, Garrus will still support and care for you. Heck, even when you break up with him he's totally understanding and remains warm to you when most people would "get in the skycar and leave".
Subverted (although this may be a retrospective way of seeing it) in Sluggy Freelance. Leo seems to be accepting of all the weird things ZoŽ tells about happening to her - but it turns out that was only because he thought she was lying. In the words of another jerk he hangs out with, "You've got to respect a girl who realizes romantic relationships are based on lies and goes to town with it!" As soon as Leo finds out it was all true, he feels betrayed, and they eventually break off.
In Teen Titans there's the episode where Starfire turns into a chrysalis, her species' own version of puberty, and Robin chases after her, even after seeing all her weird changes. Later when he meets up with her again, he tells her he would have come for her even if she hadn't changed back to looking perfectly normal. Daww...
Added on to that, while Robin is far from useless in a fight, he has no actual superpowers. Starfire is capable of flying, shooting energy bolts out of her hands, and can punch out villains twenty times her size.