Half-Orc

A half-orc is exactly what it says on the tin - an unholy fusion of man and orc, hopefully brought about by an male orc raping (or, if the native women are amicable, tenderly making love to) a female human rather than a male human having sex with a female orc (female orcs are very ugly and unfappable, if you go by Blizzard standards). Typically they get small (+2) bonuses to physical stats (STR in 3.5e) and a small (-2) penalty to mental stats (INT and CHA in 3.5e) and 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.

Basically, if you wanted to play a big, dumb, "I hit it with my axe" pure combat class, especially a barbarian, half-orc was the race for you.

Later games opened things up a little, implying that 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. Some places actually have full on half-orc populations, where man and orc have so thoroughly interbred that everyone's a half-orc. 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 and generally enjoy access to a decent array of versatility in what they try to do.

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. 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'."

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.