Alternate costume (SSBM)

Super Smash Bros. Melee used the X and Y buttons on the Gamecube controller to change costumes.

Mario

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Mario's alternate costumes in SSBM

Mario's yellow costume is based on Wario, the same as his previous yellow costume.
Mario's blue costume is a red/blue reversal of his traditional colors. This is seen as a partial reference to Mario's varying appearances in games prior to Nintendo's officially establishment of Mario's outfit of consisting of a red shirt, blue overalls and red hat. In various earlier games, Mario occasionally also appeared with sometimes a blue hat, red shirt with blue overalls or a red hat, blue shirt with red overalls. Interestingly however, Mario never appeared in any game with the particular combination of a blue hat, blue shirt, with red overalls as it appears here.
Mario's brown and white costume is a reference to Foreman Spike from Wrecking Crew.
Mario's green costume is a color inverse of his traditional colors. Contrary to popular belief it is not a reference to Luigi, however it does coincidentally resemble Luigi's colors from the arcade version of Mario Bros.

Luigi

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Luigi's alternate costumes in SSBM

Luigi's white costume is a reference to Fire Luigi from Super Mario Bros. & subsequent games after.
His red costume comes from Wrecking Crew, in which Luigi wore pink.

Peach

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Peach's alternate costumes in SSBM

Peach's yellow costume changes nearly her entire appearance to that of Daisy, including her hair color, hair style, earrings, dress style, gloves, crown and even skin color.
Her blue & green costumes imitates Mario & Luigi's caddies in NES Open Tournament Golf.
Peach's white costume imitates her Nurse Toadstool costume from Dr. Mario.

Bowser

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Bowser's alternate costumes in SSBM

Bowser's blue costume came from the international artwork for Super Mario Bros.

Yoshi

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Yoshi's alternate costumes in SSBM

All of Yoshi's costumes appear as different variations of the Yoshi species in many of his games.
Yoshi's pink costume resembles Birdo.

Donkey Kong

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Donkey Kong's alternate costumes in SSBM

Two of his costumes came from Donkey Kong 64's "Monkey Smash".

Captain Falcon

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Captain Falcon's alternate costumes in SSBM

Captain Falcon's red costume is based off his rival Blood Falcon's outfit, even altering the logo on his back.
Captain Falcon's white costume is based off the colors of Jody Summers's outfit.
His black costume possibly came from the Japanese commercial for F-Zero X.
Captain Falcon's green costume is based off the colors of Pico's outfit.

Ness

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Ness's alternate costumes in SSBM

It is possible his blue costume came from the Devil Machine's eye for the color of Ness's hat.

Ice Climbers

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The Ice Climbers' alternate costumes in SSBM

The Ice Climbers' orange and red costumes will place Nana in the lead, making Popo follow. The voice samples are swapped to match up with the change.

Kirby

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Kirby's alternate costumes in SSBM

Kirby's yellow costume is Keeby. It is also the same as when he is Beam Kirby, sans the hat.
Kirby's red costume is the same as when he is Fire Kirby, sans the hat.
Kirby's blue costume is the same as when he is Ice Kirby, sans the hat.
Kirby's white costume is a reference to his monochrome appearance from the original Kirby's Dream Land for Game Boy. Coincidentally, it is also similar to the colors of Kirby's depiction on the North American box cover of Kirby's Dream Land.

Samus

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Samus's alternate costumes in SSBM

Samus's default costume is her Varia Suit.
Samus's pink costume is based off the appearance of the Varia Suit when missiles are selected in the original NES Metroid game. It is also the color of the Gravity Suit in iterations prior to Metroid Prime.
Samus' purple costume is based on the Gravity Suit from Metroid Prime & subsequent games after

Link

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Link's alternate costumes in SSBM

Link's red costume is based on the the Goron Tunic from The Legend of Zelda: Ocarina of Time.
Link's blue costume is based on the the Zora Tunic from The Legend of Zelda: Ocarina of Time.
Link's violet costume resembles the use of the Blue Ring in The Legend of Zelda, this color would later be used in The Four Swords series.
Link's black costume is a homage to Dark Link. However, unlike the Brawl version, it is only his tunic.

Mewtwo

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Mario's alternate costumes in SSBM

Mewtwo's green costume is its "shiny" variation in from the Pokémon series.

Mr. Game & Watch

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Mr. Game & Watch's alternate costumes in SSBM

Some of his alternate costumes came from the colored LCD screens.

Marth

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Marth's alternate costumes in SSBM

Marth's white costume is based on Leaf, the protagonist of Fire Emblem: Thracia 776.

Pikachu

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Pikachu's alternate costumes in SSBM

Pikachu's red costume has it wearing the hat of Red, the protagonist of the original Pokémon installment. It's also based on a "shiny" Pikachu.
Pikachu's blue costume has it wearing a blue party hat (like the one in the original).
Pikachu's green costume has it wearing a green cowboy hat.

Pichu

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Pichu's alternate costumes in SSBM

Pichu's green costume gives it a backback similar to the one worn by Ash in the Pokémon anime.
Pichu's blue costume gives it goggles similar to the "Swimmer" class of the Pokémon series.