Abhuman
Abhuman (from ab-, "of, from, away from," human) is a term used in the Imperium of Man to refer to a stable-breeding subspecies of humanity. Although their physiology and mentality would be so different that they should technically be classified as a whole different species, all together. Officially, they are not considered mutants by virtue of their breed stability, but they are generally not treated the same way as "normal" humans -- they tend to be segregated into their own Imperial Guard units, and civilians are almost always an underclass on other worlds.
Origins
Humanity's characteristics are influenced by the conditions in which it grew up, including gravity, climate, and diet. If a population were isolated in a different environment for a long enough time, their distant descendents would be adapted to those new conditions.
During the Dark Age of Technology, humanity spread to the stars, first with slower-than-light colony ships, and then with Warp drives after the discovery of the Navigators. Some of their destination planets were very different from Earth, and when humanity entered the Age of Strife, the inhabitants of these worlds were cut off from other colonies; when contact was restored during the Great Crusade (or even later), their gene pools had diverged so far from the baseline that they could almost be classified as separate species. The Imperium spared them, though, because while they were clearly not pure humans, they were useful and no more prone to mutation than any other human.
The Horus Heresy novels mentioned that even during the high point of abhuman tolerance, formerly human populations have been purged due to achieving certain (high) levels of genetic "deviancy". The natives of Davin were shaggy creatures that were close to it, though Chaos may have had a hand in that, unbeknownst to the Imperials.
Beastmen
Beastmen (Homo sapiens variatus) are on their way to being declared mutants; as it is, the Adeptus Arbites has basically declared them an underclass, preventing them from traveling to most planets and excluding them from the Imperial Guard unless they're willing to be cannon fodder- something which many of them view as their chance to atone for the crime of being born as mutants. This will probably be for the best, since their Warhammer Fantasy Battle counterparts are one of the major parts of the armies of Chaos, but one wonders if the 40K beastmen would be less likely to fall to Chaos if the Imperium made them feel just a little welcome.
Felinids
Thanks to 6th Edition, Imperial catgirls (Homo sapiens hirsutus) are canon! They're found only on the planet Carlos McConnell and we know absolutely nothing about them whatsoever... Which is quite disappointing really. Judging by the Latin name, they are likely furries.
Navigators (Homo navigo) are your three-eyed, specialized group of psykers that helps guide Imperial Ships through the Warp, although essentially vital for the Imperium's survival, some radical groups in the Imperium declares them as heretical and a mutant. These guys are so different from the mainstream human, that they are actually classified as another species of the Human genus, and not a human subspecies, hence their scientific name. They also get their own house in the Houses of Terra within the Terran Administratum, which provides a large modicum of independent political clout within the Imperium and prevents them from being sacrificed to the Golden Throne.
Ogryns
Ogryns (Homo sapiens gigantus (sapiens being used in the loosest sense of the word) ) are transparently based on the archetypal fantasy ogre: big, strong, and dumb. They are useful as Imperial Guard shock troops because they are big enough to wreck the enemy and dumb enough to charge on command. They are resolutely loyal to their immediate superior officer, but this also makes it extremely easy to turn them to serving Chaos, as they will perform any command given to them if their commanders are persuasive enough, though their childlike faith in the God Emperor makes outright corrupting them harder.
(btw. has any heretic ever tried to make something like Astartes out of them? Dude, why isn't TG behind this!?!)
Ratlings
Ratlings (Homo sapiens minimus) used to be space halflings, but the latest edition miniatures give them hairy bare feet, making them look more like space hobbits (though both archetypes have a fair amount of overlap). They are also noted kleptomaniacs, so they've got some space kender in them, too. Their good eyesight and small size make them useful as snipers, but they are otherwise useless in a fight and their personal characteristics make them less endearing to Imperial Guard leadership, though the Guardsmen themselves usually don't mind -- they are perfectly fine with trading with Ratlings for some special equipment or extra rations, and they're well-known as the sorts of field cooks that can make three old rats, a handful of sawdust, and a stolen muddy boot taste downright edible. Also, they tend to shag like bunnies (Not shag bunnies).
Squats
Squats (Homo sapiens rotundus) grew up on high-gravity mineral-rich worlds near the core of the galaxy, and so they adapted to become short, robustly built, and adept miners. If this sounds familiar, it's because they were intentionally designed to be the space-equivalent of Dwarfs from Warhammer Fantasy Battle.
They were introduced in the First Edition of Warhammer 40,000 as a separate army to the various Imperial forces (being fiercely independent), and were mentioned sparingly thereafter, until they were written out of the background (hence the term "squatted"), but the sixth edition rulebook has written them back in again.
Saharduin
All right all right, I know they're not abhumans (yet), but can't we all wish for Saharduin to be abhumans? Who doesn't love sharkgirls?
In all seriousness, however, the new rulebook mentions Pelagers (Homo sapiens oceanus). Bam. Shark-people...or maybe Mermaids?
Other Kinds
The 6th edition rulebook also gives a number of other categorized abhuman types, although very little detail on what they actually are.
- Troths (Homo sapiens verdantus), which are restricted to the world Verdant. They sound like they might be tree or plant people.
- Longshanks (Homo sapiens longatus), sound like they are tall and lanky, and may be an entire race of gingers if their name is any indication.
- Neandors (Homo sapiens hyannothus), which are restricted to the world Hyannoth IV, and by their name, might be space Neanderthals or Caveman
- Scalies, which hail from the Underhive of Necromunda and can be loosely described as "Ogryns turning into lizardmen".