From the Super Mario Wiki
A Fireball (also written as Fire Ball) is a ball of fire that can be used as a weapon. Typically, one can only shoot fireballs if he or she acquires a Fire Flower. However, some enemies can shoot fireballs without the use of a power-up. Additionally, Mario can train himself to shoot fireballs from his hand (without using a Fire Flower). Ice Balls can be seen as a parallel to Fireballs.
Yoshi has fireball abilities as well. He uses them in Super Mario World, Super Mario 64 DS and New Super Mario Bros. Wii. In Super Mario World they can be spit by Yoshi after he eats a Red Shell. These look like Podoboos and destroy most enemies. In Super Mario 64 DS, they are in a stream of Fire Breath and are Yoshi's Power Flower power. They are also found by swallowing Fire Chomps, Fire Guys and campfires. In New Super Mario Bros. Wii, Yoshi can spit a giant Fireball by eating a fireball launched by a character with a Fire Flower power up, or from a Venus Fire Trap. This giant fireball transforms all enemies encountered into coins. In Super Smash Bros. Brawl, Yoshi spits single fireballs in his Final Smash form. Yoshi is also able to eat miscellaneous fireballs along with many other items. Other enemies, like Venus Fire Traps, Fire Bros. and Draglets, can also shoot or spit fireballs.
In the Mario Kart series, Fireballs are used as special weapons. In Super Mario Kart, Bowser would drop these items; touching them would make the driver spin out. Unlike other laid down items such as Banana Peels, however, they would move around a bit on the course. Fireballs reappeared in Mario Kart: Double Dash!!, where they are the special item of Mario (and Petey Piranha and King Boo, due to their ability to have any special item). Luigi's is a Green Fireball, but it acts the same. When the special item is used, five fireballs will be launched into the racetrack, hitting other drivers and causing their karts to spin-out. These fireballs are capable of ricocheting off walls. However, after a short amount of time, the launched fireballs will fizzle out. The Fire Flower item in Mario Kart 7 allows the racers to shoot fireballs forwards and backwards.
In the Super Smash Bros. series, Mario shoots red fireballs while Luigi shoots green ones. It is their normal B move, and it is used by the brothers in all three games. Mario's Fireballs are affected by gravity (meaning they bounce against the ground), while Luigi's shoot straight no matter what, unless it ricochets off of something in front of Luigi. Kirby can also use the Fireball move once he has sucked up Mario or Luigi, and the color and performance of the Fireball are according to which Mario Brother he has sucked up.
In Mario Superstar Baseball, the Fireball is Mario and Luigi's special pitch. It, unlike most other pitches, goes in a straight line. The ball, as the name says, turns into an extremely hard-to-hit fireball (red for Mario, green for Luigi).
In Mario Super Sluggers the Fireball sticks around as Mario's Star Pitch, while Luigi is given a different Star Pitch. Just like in the predecessor, Mario will throw the baseball at a fast speed, which makes it harder for batters to properly hit it.
In Mario Kart Wii's 2nd Competition of March 2009, Dry Bowser spat out fireballs to attack the player. He'd either fire three fireballs backwards or one fireball forward, depending on the player's racing position.
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