Fire Mario
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When Mario or Luigi come in contact with a Fire Flower, they can become Fire Mario or Fire Luigi, respectively.
This form was introduced in Super Mario Bros. were Mario and Luigi's shirts and hats would change to white and their overalls would change to their respective colors (red for Mario and green for Luigi) and they would gain the power to throw fireballs which could topple otherwise unbeatable enemies (such as Spinies) and would be the only way to defeat enemies in underwater stages. However, the form was lost if Mario (or Luigi) were to take damage.
This is one of the few forms to appear outside its introductory game but is often downplayed in favor of newer power-ups.
This form made its first 3-D appearance in Super Mario Galaxy which featured a few changes, such as the form now being time-limited instead of lost by taking damage and that the fireballs were extinguished by water.
In the Super Mario Bros. Super Show!, this form was called Super Mario or Super Luigi, while that usually is the name of the status when using a mushroom. The term "super" could just be tacked on to signify that they are stronger. Toad turned into this form in the episode "The Fire of Hercufleas". Princess Toadstool turned into this form in "The Trojan Koopa", although she didn't shoot fire.
Strangely, the comics almost never featured either form. The only appearance was in the prologue short, "The Legend"; in one panel, Luigi was shown throwing fireballs at some Beezos, but he was wearing his regular outfit rather than his Fire Luigi suit.
Fire Power Without a Fire Flower
In certain games, Mario doesn't need a Fire Flower to emit flame from his hands. In Mario & Luigi: Superstar Saga, for instance, no Fire Flowers are involved, although Mario does learn to kindle a fireball in his palms from a mysterious character found in the Fire Palace. Mario is also seen shooting fireballs classic-style in his Fire Orb, Super Flame, and Ultra Flame attacks in Super Mario RPG: Legend of the Seven Stars, which only requires that he sacrifice a differing amount of Flower Points to do so. However, it should be noted that both of these mentioned games are RPGs; games of the RPG genre rarely involve traditional power-ups. Despite this, though, Mario and Luigi have been shooting fireballs without Fire Flowers in other games, such as Super Smash Bros. (although Mario gets an optional Fire Mario color scheme in Brawl) and Mario Kart: Double Dash!! (the latter of which actually features fireballs as the items that allow Mario and Luigi to shoot fireballs themselves), although most side-scrollers continue to use the Fire Mario and Fire Luigi forms and their typical manner of activation in a way unaltered from the original Super Mario Bros.
trivia
In Super Mario bros. Fire Mario was known as firey Mario with White overalls and a red undershirt instead of red overalls and a white undershirt.