This is the main premise of the first Vampire Hunter D movie and novel, with the heroine hiring D to help her, complicated by the fact that her entire town is not only aware of the danger a Vampire Refugee can pose but actively on the lookout for them.
But subverted in the second movie. Although D and the Borghoff Brothers assume she's been carried off against her will, Charlotte Ellborne actually wants Meir Link to transform her into a vampire in order to facilitate their love affair. Especially interesting because Carmilla seems to view their relationship as a way of fostering better relations between vampires and humans .
Well, that's what she claims. In actuality Carmilla is brutal and bloodthirsty even by vampire standards, and only cares for humans for their blood. The whole purpose of her involvement in the enterprise was to resurrect herself with Charlotte's blood. Meir (Myer?) of course wasn't aware of this.
The comic 30 Days Of Night had the sheriff injecting himself with vampire blood to become a "Good Vampire" (barely controls it and he kills himself shortly after) to beat the bad guys.
Andrew Bennett from House of Mystery's "I... Vampire" series straddled the line between this trope and Doomed Moral Victor. Though he did jump at the opportunity for a cure when he chanced upon one, for most of his unlife Bennett harbored no hope of restoring himself, and was preoccupied with exterminating a bloodline of evil vampires he'd mistakenly sired, by converting his onetime lover. To survive, he bought blood by the bottle from street people.
Horror of Dracula has Harker, who in this version is actually turned into a vampire. Helsing grimly has to stake him.
Rise: Blood Hunter: Though Sadie is very determined to get revenge for her unwilling (and unplanned) vampirisation on the bloodsuckers of L.A., she slips when it comes to feeding on a poor schlub offering her a lift.
The Star/Laddie subplot of The Lost Boys. "YOU TRIED TO MAKE ME A KILLER!"
The Fly (the remake) has doctor Brundle try to reverse the onset of the creature he's becoming. He fails.
The first Blade movie had the vampire antidote for the Girl of the Week. Interestingly, it seems this cure sticks around, and at least two more characters get cured of vampirism in the sequels.
However, it can't cure the eponymous character of vampirism without taking away his nifty powers (he just uses a serum to suppress his vampiric bloodlust), nor can it cure anybody who was born a vampire. It can only cure vampirism if one contracts it via a bite.
Van Helsing, turned into a werewolf, must kill Dracula as a werewolf (as was prophesied), but Carl and Ana have to get the cure for lycanthropy to him before the stroke of midnight (as that's when he'll permanently be a werewolf). Fortunately for Van Helsing, the stroke of midnight lasts about twenty minutes.
In Ginger Snaps Back The Beginning, Ginger is given a prophecy that she will need to kill the infected child that bit her to avoid becoming a werewolf herself. In a subversion the prophecy meant that she should kill the child "before" he bit her.
Return Of The Living Dead III featured the heroine finding new and interesting ways to cause physical pain to keep from succumbing to her desire to eat folk.
In The Batman vs. Dracula, our hero finds a cure for vampirism, but it won't work on Dracula himself — just those he's turned.
Rayne from the first Resident Evil film gets bitten early on. She spends the rest of the time kicking ass to get everyone out and able to administer the cure to her. Too bad they're too late.
Lucy Westerna and Mina Harker in Dracula. For the former, it wasn't know what was weakening her till Helsing was called in. She would've probably been cured were it not for a few toomany bad circumstances. Mina is a bit more fortunate, since Dracula has to flee before he can fully transform her. She feels his presence within her to spy on the hunters. And, when confronted by the brides near the end of the story, senses the vamprisim welling up in her.
The Dresden Files features The Fellowship of Saint Giles, individuals who've been bitten by Red Court vampires, gaining a portion of their power and their vampiric blood lust. However, since they haven't actually killed anyone by feeding, they haven't turned into the horrific bat-demons Red Court vampires really are. As part of their membership, they gain magical tattoos that help them keep the hunger in check and turn darker as they start to lose control.
The Good Ghouls series — the main character gets turned into a vampire and finds out the only way to get turned back is to kill her own maker. Several problems: firstly, it has to be her who kills her maker; secondly, any vampire higher up the chain, including her maker, is immune to any frontal attack from a lower-ranking vampire, so she has to be sneaky; and thirdly, she doesn't even know who turned her. In the end she finds out who did it, but someone else kills him for something unrelated, so she's stuck as a vampire.
Igor Dolinsky in Night Watcher. Arguably, all the other "true vampires" qualify as well, as they are the ones who no longer need blood, though they aren't human anymore either (but then, neither is Igor, strictly speaking).
Kostya in the Nightwatch series is the only vampire to achieve "High Vampire" status without killing someone for blood. He became a biologist to prevent his vampirism from turning him into a monster. By the third book, he even tries to turn every human being on the planet into Others just so he could be normal. He fails
In the Ravenloft novel Vampire Of The Mists, Jander Sunstar was desperate to find a cure for his vampirism once he finally managed to become free to seek that cure; he was heartbroken to learn that there was no cure other than true death (and possibly not even then).
Moreover, his specific background makes this grimly hilarious: until mists took him, as a Gold Elf back on Faerun he was very close to the cure for undeath all those centuries. He didn't know it even exists mainly because the elves treat High Magic as the greatest secret of Multiverse even when they know it's an Open Secret to the present company, and he was just a young adventurer hanging out with humans.
Gordon had the perfect set-up for becoming a Vampire Refugee, but since he knew there was no way to undo the change, he decided instead to kill Sam and then himself. Instead, Sam killed him.
In season 6, this trope was played completely straight as Dean gets bit, angsts, kicks some ass, and then gets cured at the end of the episode.
On My Babysitter's a Vampire, Sarah (the babysitter) was turned into a vampire by her boyfriend. However, she refuses to eat humans and exists on animal blood or blood substitutes while trying to find a cure.
Mage: The Awakening features rare wizard refugees in the form of the Banishers. Banishers had their Awakening go wrong in some way or another (it's suggested more than a few of them literally gazed into the Abyss); as a result, the very use of magic causes them revulsion, and they spend much of their time hunting down and killing other mages out of the belief that magic is, at its core, evil.
In Vampire: The Masquerade, vampires would occasionally seek out Golconda, a mystical state of transcendence. Nobody could agree on what Golconda was, but one persistent rumor was that it would allow you to shake off the Embrace and become mortal again. One scenario had the villain trying to eat his way up his "family" tree to cure himself.
One of the paths in Tsukihime involves Shiki being increasingly possessed by an ancient vampire sorcerer, gaining the usual powers and bloodlust as his will rapidly erodes, and having to defend himself against his former companions. At first he holds out for a solution from the Church, but when that doesn't pan out he resorts to his solution to everything else—turning his Mystic Eyes of Death Perception on and stabbing himself in an attempt to 'kill' the vampire's soul.
Also from the Tsukihime universe, Sion Eltnam Atlasia is entirely based on this. She even goes as far as to create an alchemical substitute for blood to deal with her cravings as a temporary measure. (It works, but only because of the extenuating circumstances.)
This becomes an optional quest in The Elder Scrolls: if the hero becomes a vampire. In Daggerfall it is offered by a vampire hunter who give you a choice instead of killing you (you can also drink the potion a witch conven ask you to transport). In Morrowind, it is given by reading a book about a cured vampire and doing a favor for Molag Bal, the "patron" daedra of vampires. In Oblivion it involves collecting a long list of ingredients to make a potion. In Skyrim it involves trapping a human soul in a Black Soul Gem and giving it to a sorcerer, who sacrifices the soul to Oblivion as payment for your vampirism to be lifted.
As does the plot of Neverwinter Nights 2: Mask of the Betrayer, at least for a good-aligned character.
Vampire: The Masquerade – Bloodlines features a "thin-blood" down by the beach who's desperately trying to find a way out of his new condition. You can either a) let him down easy and tell him that he can at least try to go on (un)living, or b) bilk him for all he's worth by selling him a "stake of pure rosewood" he can use to kill the "head vampire" or some vampirism-curing "unicorn blood." Or both.