Half-Orc

A half-orc is exactly what it says on the tin - an unholy fusion of man and orc. Traditionally, such procreation is done under a male orc/female human paradigm, predominantly under connotations of rape (not explicitly stated as such, but heavily implied nonetheless). This has made the half-orc one of the more traditionally "edgy" and politically incorrect racial options, so it has almost as many haters as it did a fans; the fact that half-orcs are usually described as looking more like orcs (aka, monstrous) has further made them a somewhat marginal race even amongst edgelord players, who are more likely to gravitate towards races like tieflings or even half-elves (hey, they can be rape children too). In fact, this "child by rape" standard origin is generally held up as the reason why it's believed TSR didn't make half-orcs playable in Advanced Dungeons & Dragons until the Complete Book of Humanoids, when they had first appeared in the 1e PHB.

Traditionally, half-orcs receive a "watered down" version of the orc's traits; this amounts to a lesser Strength boost but also a lessened penalty to mental stats. From 3rd edition onwards, at least, they tended to continue this trend by having better nightvision than humans, but also better daylight vision than orcs, gaining darkvision without suffering light sensitivity. Bonuses towards intimidation-type effects, reflecting their frightening mien, aren't uncommon, and they tend to lean towards evil and chaos in settings where orcs just swing that way for reasons of giving PCs critters to kill without feeling bad about it.

Weirdly, half-orcs weren't quite in line with the aforementioned paradigm in AD&D; they got +1 to both Strength and Constitution to offset their -2 Charisma, with pureblood-orcs only getting the +1 Strength, and they had higher racial maximums for Constitution and Intelligence. Meanwhile, orcs had a higher racial maximum for Wisdom and could get to much higher levels in Cleric, Shaman, Witchdoctor and Thief than half-orcs (unless the half-orcs had exceptional ability scores). Pureblood orcs had a chance to notice new/unusual construction and sloping passages, whilst half-orcs lacked the light aversion of the purebloods. In the 1st edition Player's Handbook, half-orcs were allowed unlimited level advancement in the assassin class, ans well as the ability to multi-class as assassin/fighters, or assassin/clerics.

Later games opened things up a little, with tweaks to the fluff and the crunch.

Fluffwise, there was implying that female orcs generally aren't as ugly as people make out (after all, only male animals have tusks), and that frontier clans tend to intermarry with some frequency. Even way back in AD&D, there were occasional comments implying individuals having peaceful co-relations; the factol of the Bleakers in Planescape was the son of a blind man and his orc wife, whilst Greenwood has spoken on forums about isolated regions where human widows or spinsters have accepted displaced orc braves as, essentially, live-in hired help that accepts sex and food in lieu of money for taking care of the homestead. Some places actually have full on half-orc populations, where man and orc have so thoroughly interbred that everyone's at least a little bit half-orc. Although traditionally the result of human/orc crossbreeding, the 5e Monster Manual proclaims that half-orcs (or even pure-blooded orcs) can result from any cross between an orc and a non-orc Medium-sized humanoid, specifically calling out dwarves as a potential parent of half-orc children. This is all a matter of fluff, at the moment, but combined with their lack of racial penalties, could make for some interesting character ideas. Fourth edition also introduced more explicit ideas for racial backstories beyond "orcs like to rape and pillage", such as half-orcs being the result of deliberate intermarriage on a massive scale, crossbreeding by some external faction, or even a deliberate creation of Gruumsh the orc-god to create a superior strain of orcs to lead the rest of his children to victory.

Everyone agrees that this is in much better taste and shuts out some of the edgelord bullshit, and it's gone over quite well.

Crunchy improvements, on the other hand, came much later. In 4e, for instance, they don't take mental penalties to their stats and make pretty good monks due to their boosts to strength and dexterity. And in Pathfinder, they, like half-elves, get to pick a stat to put their boost into like humans, get to keep ticking once reduced to zero health until outright K.O.'d like orcs, and generally enjoy access to a decent array of versatility in what they try to do. If nothing else, they have access to the awesome scarred witchdoctor witch archetype. 5e went back to the old-fashioned muscle-class fodder, but actually made them excel at it, taking away their mental stat penalties in the process. Their abilities basically make them "barbarians-lite" if they're any other class, or the best barbarians in the game if one goes for tradition.

Exactly how oppressed and angsty they are varies with the setting, and, more to the point, with the setting's orcs.

When they're just traditional rampaging barbarians all the time, they tend to get all kinds of shit on -- Golarion, home of the Pathfinder setting, really plays up the "half-orcs are usually born to rape" in the fluff, so they get a lot of flak... somewhat two-facedly, though, most of their important half-orc characters are not rape-children, and in places like the deserts or the Mwangi jungle, half-orcs are actually quite respected. Desert half-orcs actually get bonuses to diplomacy instead of intimidation.

In places like Eberron, where orcs aren't so bad once you get to know them, they fare much better, though still suffer discrimination due to a perceived lack of intelligence.

Almost every setting, though, points out that anyone big and beefy enough can carve out a niche for him- or herself in among the "civilized" races, and that being the smartest motherfucker in the room an only slightly less strong has its own advantages in the orc tribes. Lots of famous orcish heroes had enough human blood in them to make them, as their spacefaring cousins would say, "ded kunnin'."

In AD&D, Half-orcs were a lot more diverse. The "basic" half-orc entry in the Monster Manual covered not only orc/human hybrids, as discussed in detail here, but also orc/goblin and orc/hobgoblin crossbreeds. Orc/ogre crossbreeding was rumored to be the source of the Orog species (although 3.5 Forgotten Realms retconned orogs as an Underdark dwelling species of bigger, smarter orcs), which itself received magically augmented/created variants in the "Neo-Orogs" of the Forgotten Realms (divided between Red ones, for fighting, and Black ones, for assassination). A confirmed orc/ogre crossbreed, though definitely leaning towards the Ogre (it was actually listed under "half-ogre" in the AD&D MM) is the Ogrillon, which basically resembles a giant orc covered in bony spikes. The weirdest half-orc is the Losel, or "ape-orc" of Greyhawk, which is half-orc and half baboon -- thankfully, that one's believed to be a magical creation, like the owlbear.