"Grimmer than these scarce any prodigy, nor any plague e'er rose at the wrath of the gods from the Stygian waves: a winged thing with maidenís face, belly o'erflowing and most foul, a hooked hand, and face hunger-pale forever."
Like centaurs, mermaids, Fauns and Satyrs, harpies are mythical creatures that take the form of Half-Human Hybrids — in this case, one half is a woman and the other half is a bird, usually a bird of prey. They originated in Greek Mythology, where they often took the job of punishing mortals for their misdeeds. This punishment frequently took the form of snatching away or befouling people's food, hence their name which comes from the Greek word for "snatcher." They also can be considered as Anthropomorphic Personifications of violent winds.
They can vary widely in appearance. Most of the time they are seen as ugly, but they were originally described as beautiful, and often are subject to the Gorgeous Gorgon effect. The ratio of human to bird can also vary from human-faced bird to Winged Humanoid. In many classical depictions, their arms are their wings. They often come in groups of three, and are often given the names of Aello, Celaeno, and Ocypete.
Related to the other mythological half-woman half-bird creature, the Enthralling Siren. Sirens and harpies are confused almost as much as sirens and mermaids, usually by giving harpies beautiful voices.
The harpy eagle is named for them, and their tendency to be Always Chaotic Evil has led the word "harpy" to be used to describe any unpleasant woman.
Harpies play a major role in the first episode of the fantasy softcore HentaiThe Elven Bride, in which the protagonist attempts to capture a traditional monstrous harpy in order to farm it for its secretions, which are rumored to be the "ultimate lubricant" that would enable him to consummate his marriage to the titular elf (the initial attempt at doing this failed due to the bride possessing an unusually small receptor). However, the attempt leads to him being abducted by the harpy's mother... A Cute Monster Girl called a Harpian.
The Mass-produced Evangelions in The End of Evangelion have picked up the Fan Nickname of "harpies" because of their wings, monstrous appearance, and vulture-like behavior.
She was seen looking like a regular human woman in flashbacks, so while it hasn't been directly confirmed, it all but seems that she really is a normal human who just had her arms exchanged with wings and legs with talons thanks to, er, magical surgery done by one of her (supposed) allies.
The Incredible Hulk: The Leader turned Betty Ross into a Gamma powered Harpy once, and in World War Hulk's "Gamma Corps", the Hulk's old enemy the Clown was turned into the Griffin with Gamma technology, specifically based on Betty as the Harpy.
They show up in Clash of the Titans (2006) as the flying, devilish minions of Hades. Although they don't resemble bird-women at all, they do serve the purpose of snatching people up and pulling them into the Underworld.
The "Great Arms" of the Imperial City of Nuremberg originally depicted an eagle with a king's head; over the decades this was Flanderized into a harpy.
Celaeno first appears alongside her fellow harpies in The Aeneid, where she prophesies that before Aeneas and his men find their home, they will become so hungry that they will eat their tables.
The Black Jewels trilogy includes them as the new forms of dead women who were killed violently by men.
Dante's The Divine Comedy puts them in hell, specifically the area inhabited by people who have committed suicide.
A rare heroic (and gorgeous) harpy, Chewppa, is the lead female protagonist of Book 5 of Grey Hawk Adventures novels.
While there's no evidence of the existence of actual harpies in the Harry Potter universe (the veela are the closest thing to them), there is a Quidditch team called the Holyhead Harpies, that's made up entirely of women.
The Solomon Kane story "Wings in the Night" has them pop up in Africa. They're called akaanas, and they like to eat people, and are notable for being the only time that Solomon Kane has gone berserk.
Xanth harpies are ugly old hags who attack via curses. The One Gender Race and Gorgeous Gorgon aspects of them are played with, in that there are a few rare male harpies who are the good-looking ones; this is explicitly (not that kind of explicit, they're not that kind of book...usually) contrasted with the goblins, which in Xanth are mostly ugly males with a few beautiful females.
Also it becomes clear in one of the novels that young female harpies are actually very pretty; it's not until they grow up that they become ugly.
Harpies are from Greek Mythology, where they seem to be personifications of malevolent storm-winds that abduct people and spread pollution and filth. They were one of the obstacles faced by Jason and the Argonauts.
Harpies appear as a flying unit for Dark Elves and Hordes of Chaos in Warhammer. They are a One Gender Race, winged female humanoid, group of scavengers and snatchers. The issue of beautiful vs ugly Harpies comes to a head since they are depicted as attractive but only from the belly up to the neck as a "parody of a woman's body".
Ariel disguises himself as one in The Tempest to deliver a message.
Most of the Castlevania games have harpies as an enemy.
God Of War had these as easy to kill but annoying enemies. They are typically seen scavenging off corpses and their behavior implies that they are not sentient. Also, like most female monster in this game, they have exposed breasts, but not very nice ones.
The Warcraft world has Harpies as enemies both in the RTS and the MMORPG.
Legend Of Mana harpies are bird-women who cause naval disasters with their singing. In one sub-quest, you bring one of the harpies that you befriend on board a ship, whose Hot Blooded captain practically orders her to sing, and It's Up to You to keep the boat from sinking by attacking the monsters that spawn as a result of said singing.
Terraria has harpies (sometimes spelled 'Harpeys') as a relatively common enemy on the heights where sky islands usually form.
The Elder Scrolls V Skyrim has an enemy that appears in certain locations called a Hagraven. It is a highly aggressive and unpleasant half-woman / half-bird creature.
Stage 2 of Maldita Castilla is called "Road of the Harpies", that's all that you need to know.
The Witcher II Assassins Of Kings features harpies as enemies, especially down this one road where you encounter hordes and hordes of them, along with a variant called erynias. One Fetch Quest has you harvesting their feathers for a merchant who is essentially a member of the Furry Fandom.