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. They also have a nasty habit of punching outside of their CR. Their regeneration is very strong and they make a large number of attacks per round. In 3rd edition especially, their rules were created to allow fighters with Cleave and elemental spellcasters to feel stronger, and characters without those abilities to be a strait disadvantage. Similarly, nearly any template put on them made them even more dangerous. Results could include Zombie, where the hydra's pseudo-pounce and very strange version of regeneration (that's technically not lost like the normal kind) negating the templates main weakness making hydras (especially pyrohydras, who can't have their heads permanently severed as zombies) a favorite of necromancer PCs, or the Monster of Legend which made them literally unkillable short of a Wish spell.
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 several more appearances throughout Magic's history, usually favoring Green over Red. While a lot of them aren't used competitively, there are plenty of notable Hydra cards, especially in recent years such as Hydroid Krasis, which gives you a load of card advantage and Progenitus, the ridiculously hard to cast WUBRG Hydra that confuses casuals.
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!