From the Super Mario Wiki
Fire Snakes (originally parsed Firesnakes) are long, snake-like Lava Bubbles with bodies made up of fireballs. They have appeared as uncommon enemies in several Mario games, mostly in Desert-themed levels.
Super Mario series
Super Mario Bros. 3
The first appearance of Firesnakes is in Super Mario Bros. 3, where they appear in Desert Land. If a Firesnake sees Mario, it begins to chase him by bouncing and trying to collide with him. A Firesnake can only be defeated by either hitting it with a Shell or Hammer, by having Mario touch it while he is empowered by a Starman or by having Mario whack it with his tail as either Raccoon Mario or Tanooki Mario or a stomp from Statue Mario. He can also make them to fall into an abyss, however, they reappear after a few seconds. In the original NES version, Firesnakes do not have eyes, whereas they have them in Super Mario All-Stars and Super Mario Advance 4: Super Mario Bros. 3.
Super Mario World
While Firesnakes did not appear in Super Mario World, a subspecies called Bound Fire did.
New Super Mario Bros.
Fire Snakes also appear as uncommon enemies in New Super Mario Bros. in the stage 2-5. These Fire Snakes will try to attack Mario by chasing him by bouncing and by trying to touch him, like in Super Mario Bros. 3. The Fire Snakes of New Super Mario Bros. can be defeated by throwing a Shell at them and by touching them when Mario is empowered by a Starman or Mega Mushroom. He can also make them to fall into an abyss, however, they reappear after a few seconds. They only appear twice. They are depicted with eyes similar to re-releases of Super Mario Bros. 3.
New Super Mario Bros. Wii
They also appear in the game New Super Mario Bros. Wii acting like they did in New Super Mario Bros., but they have a new ability. After one or two hops, their heads will enlarge, then go back to normal size. They only appear in World 2-3 and can be defeated with a Starman or ice balls.
New Super Mario Bros. 2
New Super Mario Bros. U
Fire Snakes reappear in the Wii U title New Super Mario Bros. U acting exactly as in the predecessors. They have their own level called Fire Snake Cavern located in Layer-Cake Desert in which they are very common alongside the Fire Bros., and can now be eaten by any Baby Yoshi.
The Adventures of Super Mario Bros. 3
Firesnakes make a few minor appearances in The Adventures of Super Mario Bros. 3.
Princess Toadstool for President
Crimes R Us
In "Crimes R Us", the Koopalings break in to the Mushroom Kingdom Treasury, using a Chain Chomp to open the barred window, a Ptooie to blast a hole in the wall, and a Firesnake to bust a hole in the roof.
Nintendo Adventure Books
In Double Trouble, a swarm of Firesnakes can be encountered in the Koopahari Desert if Mario decides to take a shortcut to Fort Koopa. Depending on how an accompanying puzzle is solved, Mario either dodges and escapes them, or is sent running after being singed twice, losing his Super Mushroom in the process. Far fewer Firesnakes can be encountered on the main road to Fort Koopa, and Mario can easily avoid them.
Two Firesnakes appear as competitors in the International Mushroom Games in Leaping Lizards, being members of a team called the Sneaks. During the Beetlebowl, an all-team game, they may (depending on who the reader chooses as their offensive line) leap into the middle of the ring when the event begins and flare up, blinding everyone nearby besides Roy Koopa and their Rocky Wrench teammate, due to their sunglasses. When one of the Firesnakes grabs a Hoopster and tries to dunk it into the Mushroom Kingdom Royals's bucket, Mario unintentionally stops it when the Mushroom King (who had been turned into a rabbit) hops by, causing him to sneeze and blow the Firesnake out. What other events the Firesnakes compete in besides the Beetlebowl are unspecified.
In Koopa Capers, Wendy O. Koopa, needing some Firesnake scales for a potion she is brewing, captures several and locks them in a freezing cave in the Magma Pits, causing them enter a catatonic state and begin shedding.
Mario Kart series
Mario Kart DS
Mario Kart Wii
Fire Snakes also appear in Mario Kart Wii, acting the same way as they did in Mario Kart DS. They appear on two courses; one of which is Desert Hills from Mario Kart DS itself. They also appear in Grumble Volcano where they are found near the end hopping out of pipes on the side of the course, attempting to spin out any racers that touched one. They now have eyes on their heads, as in the Super Mario Bros. 3 remakes.
Mario Kart 8
Fire Snakes reappear in Mario Kart 8 as obstacles for the racers on Grumble Volcano, which returns from Mario Kart Wii.
Names in other languages