From the Super Mario Wiki
Though often used by Mario, Bowser, and other characters as means of attack, fireballs (also called Discs or swirls) are sometimes encountered as stand-alone obstacles. The first appearance of fireballs in the Mario franchise, Mario Bros., is also the first time they were depicted as independent enemies.
In Mario Bros., fireballs are unique enemies in that game in that they cannot cross the left or right edge of the screen and come out on the other side. Together with Icicles, they are also the only enemies that can harm players hiding behind the bottom pipes.
If the player takes too long to clear a phase, a fireball will appear to impede the player. Fireballs come in red and green varieties. The red fireballs are slower and bounce diagonally all around the stage. If they hit one side of the screen, they ricochet off the side and keep going until making a full circuit of the screen after which they will disappear and respawn as a faster opponent. The quicker green fireballs move horizontally from one side of the screen to the other where it will disappear until respawning elsewhere. It has a pattern of two small wavy bounces and one long bounce. Typically, the green fireballs spawn on a row where a player is located. To destroy fireballs, the player has to bump them from below while they are touching the platform, or use a POW Block. Fireballs respawn as faster enemies a few moments after being destroyed. There can be a maximum of four fireballs, two of each color, on screen at any one time.
In other iterations of Mario Bros.
In the Atari 2600, Atari 5200, Amstrad CPC, and other ports of Mario Bros., only the red type appears.
In the NES port of the game, fireballs are significantly smaller, making them easier to avoid.
In Super Mario Bros. 3, there is a two-player minigame that has fireballs in it. In Super Mario All-Stars, the Battle Mode has both fireballs using the red sprite, while the battle game unusually replaces the sprites with Boos. Red fireballs can also now go through the wrap-around screen.
Fireballs appear in Luigi Bros., an additional game featured in Super Mario 3D World. Like the other enemies in Luigi Bros., fireballs behave in the same way as Mario Bros., which this game is based on.
VS. Wrecking Crew / Wrecking Crew
In VS. Wrecking Crew and Wrecking Crew, a red fireball will appear if too much time is spent in one place. It behaves like the green fireballs of Mario Bros. but with a simpler wavy pattern. Careful positioning can allow the fireball to fly harmlessly over Mario or Luigi's head.
Mario Power Tennis
The green variants of Fireballs based on their Mario Bros. sprites appear in Mario Power Tennis in the minigame Coin Collectors as obstacles bouncing around the court. If a player comes into contact with one, it stuns them for three seconds as the defeated sound effect from the original game plays.
Super Mario Galaxy games
In Super Mario Galaxy and Super Mario Galaxy 2, fireballs move in circular patterns, either through the air or coming out of lava, appearing as an arc. They appear in places like the Freezeflame Galaxy, the Melty Molten Galaxy, the lava pool in the Freezy Flake Galaxy, and the Melty Monster Galaxy. Unlike most depictions, these fireballs have long, burning tails. A small, rolling variety can be spawned by Magikoopas, and in the former game, is in fact the only thing generic Magikoopas can spawn in gameplay.
WarioWare: D.I.Y. Showcase
A green Fireball appears as a recolored fireball sprite from Super Mario Bros. in WarioWare: D.I.Y. Showcase. It appears in 18-Volt's boss microgame Dustpan as an obstacle that roams on the stage and must be avoided.
Donkey Kong Country series
Donkey Kong Country Returns / Donkey Kong Country Returns 3D
In both Donkey Kong Country Returns and Donkey Kong Country Returns 3D, fireballs are featured as hazards during a short section of Hot Rocket. They come out from behind and fly across the screen, destroying the Kongs' Rocket Barrel and causing them to lose a life if they come into contact. However, if avoided, fireballs simply outrun the characters, never to be seen again. Fireballs cannot be stopped or destroyed. At one point, a fireball crashes into a chunk of rock falling from the ceiling, destroying it and revealing a Puzzle Piece.
Donkey Kong Country: Tropical Freeze
Fireballs that drop from scorching baobabs appear in Scorch 'n' Torch, a level from Donkey Kong Country: Tropical Freeze. They spawn regularly from the canopy and come down in a straight line, always disappearing in a pit below. The Kongs would have to time their jumps so as not to get hit and damaged by the obstacles. Fireballs can only be dispelled using Water Sacks.
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