Alucard from Hellsing is a Hunter of His Own Kind. Father Alexander Anderson, who operates both as a Paladin and Holy Hitman, is this trope played straight. Their employers, the Anglican Church's Hellsing and the Catholic Church's Iscariot, are entire organisations of monster hunters.
Abel Nightroad of Trinity Blood...okay, this isn't fun any more. Although, to Abel's defense, he isn't actually a vampire, but a member of a vampiric race of vampire hunters (who drink vampire blood like the vampires feed on humans), Crusniks, which is exactly three individuals strong with one more long dead.
Himegami of A Certain Magical Index (also known as Deep Blood) smells delicious to vampires, but her blood kills them when they try to feed. In a standard subversion, she hates the killing, and wants to never use her power in that way again. In a not so standard subversion, no one is quite sure if the people she is attracting and killing are actually vampires. It's never confirmed one way or another.
Baron Vordenburg in Carmilla is one of the earliest examples of literature, possibly the Trope Maker.
Most modern examples are descended in part from the character Abraham Van Helsing in the original Dracula. Van Helsing was never described as a vampire hunter in the novel, though; he was merely a doctor with knowledge of exotic diseases. It's never explicitly said, but Van Helsing clearly demonstrates perfect knowledge of vampire weaknesses and is instantly willing to make use of his knowledge after noting that Lucy's symptoms match those in the legends, without so much as a hint of skepticism. This would seem to imply that he has some previous experience with vampires or other supernatural phenomena, even in the original novel.
The night teams in Night Watcher are a secret/informal government/municipal initiative for just this. Arguably subverted in that they generally work with the vampire conspiracy against the more feral vampires and mostly aim for population control; though the ones actually seen in the book (two cops, later joined by a journalist, a psychic werewolf, and a vampire that has overcome his craving for blood and helped by The Mafiya) seem to be keen on making this a Double Subversion.
Played with in The Saga of the Noble Dead. Magiere and Leesil are con-artists and partners who pretend to be a Vampire Hunter and a vampire respectively to gull superstitious peasants out of their money - until a chance encounter with the real deal and the subsequent revelation that Magiere is a Dhampyr cause "the game" to turn deadly earnest.
Night World: Rashel was a little kid. Then a vampire killed her mother and brother. Then he tried to come back for her and killed her vampire. While we are dealing with a world where not all vampires are evil, the fact that she tracks them by the trail of corpses means she only finds the bad ones anyway. Rashel is scary good at what she does until she loses her zanshin. Then she's just very, very good.
In the novel version of I Am Legend, Robert Neville is clearly hunting vampires.
Carlisle Cullen of Twilight was one of these before becoming a vampire himself.
Most of the witches (other than the Smoke line) in the Den of Shadows series are vampire hunters.
This is the calling of the Slayer in the Buffy the Vampire Slayer series. Slayers, in addition to fighting vampires, also have to fight demons, which vampires are something of a subset of in the Whedonverse.
Angel falls into this category as well, both on Buffy and his own series.
Monsignor Javier Mendoza in Blood Ties is a villainous variant. He was a Grand Inquisitor during the Spanish Inquisition, who captured vampires using any means possible, tortured them until they confessed, and then brutally executed them. Oh yeah, he also used their blood in a potion that stopped his aging process, allowing him to continue the hunt. He doesn't shy away from murdering innocents to get to his prey. In "Heart of Ice", he murders a prostitute and drains her of blood, so that Henry's friends would give him up.
Interestingly, the only anti-vampire weapon they show him having is a sun-shaped Chinese-made object that weakens a vampire to the point of a human being stronger. The object has to be physically attached to the vampire's chest to work, requiring trickery, given the vampires' speed.
An episode of Sliders has the eponymous characters slide into a world where vampires are real and the world knows about them (vampirism is a felony). Quinn meets a man whose wife was turned by vampires. His goal becomes to find and "free" her, so he arms himself with the usual weapons: garlic, holy water, stakes, stake-firing crossbows, etc.
Ray the werewolf hates and attacks vampires on the American version of Being Human, though it's less righteous crusade and more fang-bashing.
The original has McNair, who travels around Britain with his son, hunting vampires. A somewhat unusual example as both of them are werewolves.
Forever Knight had a dhampyr-type hunter in the episode "Bad Blood". He wasn't a vampire's child, but had dhampyr-type enhanced abilities due to not being completely drained by LaCroix years before.
Alaric Saltzman - The good version who only goes after evil vampires.
"Uncle John" Gilbert - The morally ambiguous version, who goes after ALL vampires... except Isabel.
In the flashback segments, Jonathon Gilbert (distant relative of Uncle John) seems to have been a vampire hunting badass of the "they ALL must die" variety back in 1864. He "invented", with some help from Emily, several weapons and devices that can help him to easily locate and destroy vampires, many of which reappear in the modern setting.
Bad guy Connor Jordan and Elena's brother Jeremy Gilbert are part of the Brotherhood of the Five, which are sworn to kill all vampires. The Brotherhood was brought together by a witch and given supernatural powers and a map to a cure to vampirism.
Hunter: The Vigil features hunters that will likely target vampires at some point. However, more true to the spirit of the trope are the Cainite Heresy, the remnants of an ancient Roman cult headed by a vampire who is very pissed off at being tricked. They've found a way to use a derivative of vampiric blood magic, favor terrorist tactics, and have adopted "Who is Cain?" as their motto.
Rudolph Van Richten, the iconic hero of Ravenloft, made it his life's work to eradicate all vampires ever since one of them turned his son, forcing him to mercy kill the boy. Since starting his quest, he also became an expert on all kinds of supernatural creatures, from werewolves and zombies to liches and The Fair Folk.
A common Epileptic Tree in the Touhou fandom (brought up in, if not especially supported by, canon) states that Sakuya Izayoi was once one of these before meeting and being defeated by Remilia Scarlet.
Due in part to the sheer broken-ness ofSakuya's power when not bound by the Spell Card Rules, there is also the theory that Sakuya initially set up to hunt down the Scarlet sisters but spared them as they look (and often act) like children. Still not really supported by canon, but it explains her silver knives and why she seems more like a babysitter than a servant sometimes.
Rayne from BloodRayne is a dhampyr who hunts down vampires in hopes of finding and killing her fully-vampiric father.
The Skyrim: Dawnguard DLC has the Dragonborn either join or oppose the eponymous group of vampire hunters.
Grünfeld Bach and the Order of Leopold in Vampire: The Masquerade – Bloodlines. He serves as one of the later bosses in the game: Fairly impressive for a baseline human up against an immortal horror (you).
Blip has their resident Friendly Neighborhood Vampire tangle with a Mexican vamp hunter at one point. Immediately afterwards, she get captured and imprisoned by "Vlad", who apparently has a "judge/executioner gig" and may or may not be a vampire himself.
Parodied in thisCyanide and Happiness comic. Jack Recker thinks he's a vampire hunter. Turns out he's just a serial killer who targets Goth kids.
A minor character from Girl Genius is Dame Aedith, a vampire huntress tagging along with Master Payne's Circus of Adventure. Tragically, despite all the weirdness of the setting, there doesn't seem to be any vampires for her to hunt. But if any ever show up, she's ready!
One of Riff's customers is Kent's uncle Arminius Vambrey, a real full-time vampire hunter, who's good at what he does (no vampire except Philinnon has survived a confrontation with him) but so paranoid about vampires that he has trouble doing anything else.
There's also Muffin the Vampire Baker, who thinks vampires need to be killed by baking them in an oven due to a mistranslation in some old texts.
Vamp You loves these guys; they make great victims.
There were in fact many actual examples of "vampire hunters" in history. Naturally these men were almost invariably charlatans, often claiming to have mystical powers and/or be a dhampir. For instance in the Balkans it was commonly believed that vampires were invisible during the day, and only a dhampir could see them. A dhampir vampire hunter would walk out into a public street and pretend to wrestle an invisible creature to the ground, and then demand payment after the "vampire" had been "killed".