Hydra
Hydras are multi-headed dragon-like monsters originating from Greco-Roman Mythology. Described as a many-headed, poison-spewing serpent that could regrow its heads as fast as Hercules hewed them off, it was natural that such an iconic monster would go on to appear in other fantasy games.
D&D Hydras
The hydra has been around in Dungeons & Dragons literally since the beginning, having appeared in the Basic Set in 1977 and then going on to appear in the 1981 and 1983 Expert Sets, the 1991 Rules Cyclopedia, and then every Monster Manual from 1st through to 5th. Whilst various details have changed across the editions, the core has remained; hydras are quadrupedal, wingless dragon-kin who possess multiple heads on long, serpentine necks. They can regenerate, and favor swampy environments.
Traditional variants of the hydra include the flame-spewing Pyrohydra, and the frost-spewing Cryohydra.
Warhammer Hydras
Hydras have been a mainstay monstrous unit of the Dark Elves of Warhammer Fantasy. They are extremely tough and vicious creatures that can regenerate and spew fire, but also stupid creatures that depend on Druchii beastmasters to keep them under control.
Magic: the Gathering Hydras
Hydras have been in M:tG from the very beginning, with Rock Hydra, a card that was discontinued for being both terrible and needlessly complicated. WotC attempted to replace it with Balduvian Hydra, which epically failed because the new card was just as complicated and very slightly more terrible (due to being vulnerable to toughness-reducing effects). Hydras made three more appearances, always as red cards - first Spitting Hydra, then Molten Hydra, and finally Ancient Hydra - but never really caught on.
Monstergirls
Ironically, hydras may be the dragon-type monster least likely to get the monstergirls treatment. Even the Monster Girl Encyclopedia doesn't have a version yet!