Centaur
A race of monstrous humanoids, originally from Greek mythology, best known for being a literal mix of man and horse - they have a human's upper torso (that is, the body from the top of the hips up to the top of the head) replacing the head. They appear in various fantasy settings throughout the world now.
Centaurs invite ceaseless argument over whether they count as monstergirls or as furry. On the one hand, they do have human-like heads and not muzzles (though Japanese hentai seems to like portraying them with horse ears instead of human ears, and this has become more common in western art too). On the other hand, they have horse-junk at their business end (except, again, for some Japanese hentai, where they have human pussies at the front of their horse bodies instead or in addition to mare-cunts at their ass-end), which makes them in many ways more like bestiality than regular furries.
Not helping things is that both sides of the divide have embraced them. In fact, centaurs are so popular that the idea of replacing the horse with other critters that sound cool or sexy; lions, wolves, tigers, spiders... heck, lamias can be described as "centaurs that are half-snake instead of half-horse". The idea is so popular that a whole new word (arguably descended from the furries), "tauric", has popped up as a shorthand for it.
/d/ alternatively loves them (because they're an excuse for pictures of huge buff guys with huge horse cocks, monstergirls with huge-ass tits, or monstergirls with huge-ass tits AND huge horse cocks) and loathes them (because of the aforementioned furry/bestiality connotations).
Who were they?
The Centaurs, as mentioned above, were a race of mythical creatures from Greek myth, noted for being horny bastards and massive drunks. They were one of the less important monsters of their myths, with only a handful of references.
In their creation myth, the centaurs were descendents from a mythical culture called the Lapiths, via their douchebag king Ixion. In short, after being forgiven by Zeus and brought to Olympus for a dinner party after murdering his father-in-law by roasting him alive, Ixion started eying Zeus's wife, Hera. Zeus got suspicious, so he made a double for Hera out of clouds, called Nephele, and had her take Hera's place serving Ixion some dinner. Ixion promptly attacked and raped Nephele, for which Zeus smote his ass with a lightning bolt, then tied his spirit to a burning wheel and sent it spinning endlessly through the "sky" of Tartarus. Nephele got pregnant and she gave birth to the Centaurs.
Ironically, one of the Centaur myths describes their interactions with the Lapiths. The Lapiths invited the Centaurs to one of their weddings, and then things went haywire very, very fast. Though the Centaurs had been benevolent beforehand, the copious amounts of wine being served got them all drunk, which meant they turned on a plate during the wedding, trying to rape the women and kill the men of the Lapiths. This ended up as one huge brawl, ending with a Lapith victory. This was the Greek way of saying "Hey, nature? You suck.".
Chiron, a great healer and teacher of heroes in Greek myth, was a rare case of a friendly centaur.
A centaur was also responsible for slaying Hercules (or, to give him his original Greek name, Heracles). He tried to kidnap Hercules' wife, and Hercules shot him with one of his poisoned arrows for it. As he was dying, he told Hercules' wife to secretly soak a cloak in his blood, promising that if Hercules' eye started to wander, all she'd have to do is make him wear it and he'd fall back in love with her. The dumb bitch believed him, but the gory cape was actually poisonous and drove Hercules so mad with pain that he burned himself alive on a funeral pyre to find relief.
If you want to know about the real world origin of the Centaur, well consider where Greece is. Go too much farther north and your hit the Ukrainian and Russian Steppe where the horse was first Domesticated and where nomadic tribesmen practically learned to ride before they could walk. It's believed that the early Greeks saw either early horsemen or the first horsemen at a distance and could not understand that there looking at a human ON an animal, (a distinction that the Spanish report the Aztec had trouble grasping) and instead saw a horse with the top half of a man. Hence the origin of the Centaurs.
Warhammer 40K
Though the Centaur in and of itself haven't been discovered as of yet in the dark millenium (it is perfectly possible that they exist somewhere in the galaxy, mind you - there is weirder shit out there), the Interex had a heavy infantry platform which had the shape and appearance as the Centaurs of myth. The human soldier was fit into the front of a mechanical, horselike body, (where the head would've been on a real horse) so only the upper body was visible - They even went so far as giving the soldiers laser-crossbows.
There was an imperial guard short story. I don't remember the name of it now but it had to do with a guard officer marooned on a feral world with 3x gravity. He got caught up in a local war between the emperor warhsipping centaur natives and their Khorne worshipping enemies. Apparently the Centaurs were some kind of abhuman or whatever similar to the first settlers of Fenris. They were blended with a horse body and super heavy duty muscles to help them survive the gravity.
Though most would argue that this was freaking awesome, they were exterminated by the Imperium, and as far as we know, the Mechanicum haven't kept anything from the Interex... But who knows, maybe the next Imperial Guard Supplement will include cyborg horse-human hybrids (of course you can make these anyway and just proxy them as rough riders on the table top). You can't know with GW these days.
Also, the Zoats.
Warhammer Fantasy
The closest example fantasy has for Centaur are Centigors. A type of Beastmen whose upper part is that of a Gor(humanoid goat), and the standard lower horse part. Centigors are the Beastmens primary cavalry unit, they are good as shock troops and charging into the fray at lighting speed. Now if only their stats match their lore.
If thats not enough then things get bigger. With Dragon Ogres, because regular centaur isn't awesome enough. Dragon Ogres have the upper part of an Ogre and their lower parts are four dragon like legs. These Ogres made a pact with the Chaos Gods that they would serve them, in exchange for immortality(at the cost of having no female Dragon Ogres to fuck with). They are one of the oldest creatures in the Old World, and are supercharged when struck by lightning. The oldest and largest Dragon Ogres are Shaggoths.
In between those two are the Bull Centaur, which are half Chaos Dwarf and half bull, which are the result of worshiping of Hashut, the bull Chaos God. They are big, mean, muscular, and have curly beards like the rest of the Chaos Dwarfs.
Dungeons & Dragons
Centaurs and other "tauric" creatures have appeared throughout the editions and settings of Dungeons & Dragons, from the half-lion wemics of Forgotten Realms to the driders that have become so iconically linked with the drow.