Character Unlock: Dr. Mario To unlock Dr. Mario, you must complete 1-P Classic Mode using Mario at any difficulty/stock and without continuing.
Character Unlock: Falco To unlock Falco, you must complete the 100-Man Melee mode. Defeat Falco after you complete that, and you can play as him.
Character Unlock: Ganondorf To unlock the evil Ganondorf, complete Event 29. You will then be challenged by Ganondorf; defeat him and you can play as him from then on.
Character Unlock: Jigglypuff To unlock Jigglypuff, simply complete the game in 1-P Mode at any difficulty/stock (Adventure or Classic).
Character Unlock: Luigi To unlock Luigi, in Adventure Mode, complete the stage with a 2 in the seconds meter (03:12:43 for example). You'll then view a scene where Luigi comes and kicks Mario away so he can fight you with Peach. Defeat them both, finish the game. Defeat luigi
Character Unlock: Marth To unlock Marth from the Fire Emblem series, complete Classic mode with all 14 regular characters (not ones you've unlocked). Marth will then challenge you; beat him to gain him as a selectable character.
Character Unlock: Marth - method 2 Alternatively, you can simply use every character as a human player in VS. Mode, and get a challenge from Marth that way.
Character Unlock: Mewtwo To unlock Mewtwo, play in VS. Mode for either 20 hours (Combined VS. Play Time total), or play 700 matches in that mode. After either requirement is met, Mewtwo will challenge you; beat him.
Character Unlock: Mr. Game & Watch To unlock Mr. Game & Watch, you must complete both Classic and Adventure 1-P mode or the Target Test with ALL characters at any difficulty/stock, regular and hidden (that includes Mewtwo). After you do that, you'll be challenged; win this battle.
Character Unlock: Mr. Game & Watch - method 2 Alternately, play Vs. Mode more than 1000 times.
Character Unlock: Pichu To unlock Pichu, complete Event 37 (Legendary Pokémon). Pichu will challenge you; win and you'll be able to play as Pichu!
Character Unlock: Roy To unlock Roy, also from the Fire Emblem series, complete Classic Mode using Marth at any difficulty/stock. Roy will challenge you; defeat him and you can play as him.
Character Unlock: Young Link To unlock Young Link, complete Classic mode with 10 different characters at any difficulty/stock. You'll then be challenged by Young Link; defeat him.
Donkey Kong Junior (Complete Classic with all 25 characters.
Captain Olimar (Load SSBM with a Pikmin save on your memory card)
Celebi (See Celebi in your Poké Ball)