Harpy

They have power over the loins of men.

Yet another Greco-Roman mythological monster that has deeply embedded itself into /tg/ culture, harpies are a race of avian women who made their mythological debut in the story of Jason and the Argonauts, where they tormented a blind blasphemer of a king whom Jason had to rescue in order to find the Golden Fleece.

Harpies are best known for being "half woman and half bird", but since the myths are kind of unclear about how that works, there's quite a diverse array of possible interpretations that have popped up:

1. - A giant bird with a human woman's head, and sometimes boobs, sort of like the traditional depiction of the sphinx.
2. - A human woman with bird-like wings and the legs & tail of a giant bird.
3. - A human woman with bird-like legs and wings instead of arms.
4. - A centaur-like creature, in which the upper torso of a human woman replaces the head of a giant bird.

The second and third form choices are the most common.

There's also the argument about whether or not harpies should be hideously ugly (or at least old crones), or beautiful. Naturally, most people prefer that they be beautiful.

Because the Greco-Roman myth of the Odyssey also features bird-women with hypnotic voices, the Sirens, it's common for harpies to be portrayed as having hypnotic voices or just being good singers, despite the fact that "sirens" are often mistakenly lumped in with merfolk these days.

Dungeons & Dragons

A classic monster in Dungeons and Dragons, the Harpy is at once a perfect horror; beautiful and horrible all at once. Known for their ability to sing and draw prey, inexorably, towards them, they are notoriously sadistic and have a well-deserved reputation for playing with their prey in an excessively cruel way, only killing it when they've gotten their rocks off by subjecting their "plaything" to unspeakable torments.

Avian Dark Eldar for the win, really. They can pose a serious threat to low-level adventuring parties, except in 4th Edition, where they're kind of useless as anything but a speed-bump, like most monsters in 4E.

Traditionally, D&D harpies are fucking ugly, with the AD&D version being a cranky, weathered old hag and the 3.5 version being a withered crone-bat. 4th edition made them more attractive, essentially winged elves with clawed hands & feet, but the 5th edition artwork basically slid back towards the "ugly" side of things.

Pathfinder

To troll any monstergirl fans who might be into the setting, Pathfinder explicitly made its harpies rather good-looking, but gave them three very important negative traits.

1. They have absolutely no sense of hygiene, meaning they never wash or clean themselves. As a result, they stink to high heaven of blood, shit, rotten meat and worse. Fortunately, they can be taught to bathe themselves, and it's mentioned some harpies make dangerous urban predators simply by learning to get rid of their distinctive odor.
2. Being Chaotic Evil means they are very rough lovers, often outright sadistic; sex with a harpy is often a very painful, humiliating experience. Still not bad enough? There's trait number 3...
3. Sexual cannibalism. In Golarion, harpies eat their partners after they're done screwing them. This is usually done for shits 'n' giggles after just casual nookie, meaning you might survive a casual fling with one, but their messed up culture declares that any harpy who does not eat the father of their child is a weak slut. Which means that if the harpy wants a baby, the daddy is going to be a post-coital snack once she's knocked up.

All the same, they're still sapient creatures, and one adventure tree explicitly allows the PCs to take one on as a sidekick and help her get over her "bad habits."

Pathfinder also has the Siren species; these are a Chaotic Neutral race who appear as giant eagles/hawks/owls with the faces of beautiful women. Being all-female like their "cousins", they need to grab human men to procreate; unlike their harpy kindred, sirens are actually a very devoted and loving race. Yes, they will kidnap potential husbands in addition to just trying to seduce or rescue-romance them - they're Chaotic Neutral, after all - but they treat them well and fall very deeply in love. So much so that they've been known to commit suicide, or outright die of heartbreak, if the man they have their eyes on is stolen away or resists their charms. They have a very powerful magical song that can be used to captivate, fascinate, charm or put to sleep those who hear them, can use the Bardic Performance ability of a 4th-level Bard, and can cast Cause Fear, Charm Person, Deep Slumber and Shout as spell-like abilities, each one being usable thrice per day.

Living With Monstergirls and the Monstergirl Encyclopedia

While monstergirl harpies tend to be kinder and much more gentle than the classical sort, Harpies have a much deeper and more sinister reason for luring individuals off - they need males (preferably humans) to breed during the mating season. Though they will let a mate go once their mating season is over unless it's a black harpy. Competition between Harpies for mates is fierce, and a Harpy will go to extravagant lengths in order to impress a mate and win them away from a rival. In the Living With Monstergirls series, a Harpy's lover takes her out to the fields to exercise her wings every now and then, an activity which usually gets her amorous enough to enjoy "quality time" with her betrothed.

Harpies in Terraria

RUN, BILLY, RUN!! SAVE YOURSELF!!

Harpies are one of the more dangerous enemies in Terraria, though not one of the more powerful. Encountered at high altitudes far from the initial spawn, these free-flying fiends are largely considered Terraria's equivalent of Dwarf Fortress's infamous Carp in that they exist to ruin your shit.

With 100HP, they're one of the most durable normal enemies, and they tend to appear in large groups (often 5 or more; god help you if a Blood Moon's going on when you're in their territory). They do a huge amount of damage (nearly as much as Terraria's feared Demons), fly very quickly (making them rather hard to hit without long-range weapons), and fire volleys of feathers off in strafing runs as they zip around the area. They only appear high in the air (and even then, far from the starting spawnpoint), but they can turn any attempt to build at high altitudes into a frustrating and frequently-fatal endeavor.

Trying to build a curtain wall at the edge of an island whilst under siege from 4-5 of these fiends will result in an immediate need to roll for Anal Circumference. Whilst most well-known for their ability to knock you off ledges and bridges and sending you hurtling to a horribly mangled death on the ground far below from fall damage, they are far more dangerous if, god help you, one manages to get inside your base, where they can set about crashing into you, killing important NPC Shopkeepers, and in most ways doing a bang-up impression of a Dwarf Fortress Carp. That flies. And shoots.

Almost d'aaaw enough to make you forget that they want to slit you open and feast on your innards.

Fucking Harpies.

It's not all bad news, though - Players who build their homes high in the sky will frequently come to enjoy the safety and security that comes from having flocks of the goddamned things swarming around their base at all times, providing a constant diversion and harassment against any foe bold and foolish enough to approach in PVP maps. Harpies can't burrow or teleport (like a lot of monsters that otherwise occupy dangerous terrain in Terraria), so a walled-in area with reinforced walls will generally keep the fucking things out of your home, and provide you with useful guardians all in one stroke. Sadly, this means you need to actually build a base in Harpy territory, which is easier said than done. Harpies also have a rare chance of dropping a Large feather which can be used to make Harpy Wings in Hard mode which surpass the Angel and Demon Wings in terms of flight range. The Normal Feathers can be used to create Featherfall and Gravitation Potions, which when before you can get the Lucky Horseshoe, makes it much easier to navigate the skies to find more islands.

Note, however, that once you reach Hard mode, the Harpy is no longer the premier threat of the game, especially if you build bases in the air. The Wraith is a far more ubiquitous and annoying threat, freely moving through walls, dealing ten fucktons of damage with each hit and easily obliterating your NPCs. Evil Clowns answer the age-old question of what could happen if there was a monster equivalent of a TNT-spamming jackass on your server, throwing bombs and destroying structures. But by far the worst of a very bad lot on Hard mode is the Wyvern. With over 4000 HP, the ability to go through walls, and one of the highest damage values in the game, Wyverns are the Carp of Terraria's Hard mode - such is their power, in fact, that they cause the Harpies to say "fuck this" and start flocking at lower altitudes; you'll start seeing them the second you crest a low hill.