Falco Lombardi:
Beat the 100 man spar.

Dr. Mario (clone of Mario):
Beat Classic Mode with Mario or play Adventure Mode without losing a life, you can even play on Very Easy mode. Dr. Mario will challenge you at the end of the credits, beat him, and he's earned.

Free New Character:
Play 100 versus rounds (easy way: set it to 1 life and fall of the edge every time)

Pichu (clone of Pikachu):
The easiest way to get Pichu is to clear Event 37, or you could also play 200 VS. matches.

Marth:
To get Marth, you only need to play V.S. mode once with all origional characters (having one life and dieing does count). After playing with all characters, Marth challenges you. Or... Clear 70 VS. Matches. Marth will challenge you after you are finished. Beat him, and he's playable.

Roy (clone of Marth):
After earning Marth, beat Adventure Mode (Use Marth.) Roy will challenge you after you are finished, beat him, and he's playable.

Young Link (clone of Link):
Beat Classic Mode with 10 characters. Young Link will challenge you after you are done. He will be playable if you beat him.

Subcon (Mushroom Kingdom 2):
Earn the Birdo and Pidgit trophies.

Mewtwo:
Have a combined total time of 20 hours, or you can play 700 Vs. matches.

Mr. Game & Watch:
Beat Adventure Mode with all 24 characters.

Battlefield Stage:
Beat the game in All-Star mode.

Big Blue Stage:
Fight over 150 multi-player matches.

Brinstar Depths Stage:
Fight over 50 multi-player matches.

Congo Jungle Stage:
Beat the game in 15 Minute Spar mode.

Dream Land Stage:
Beat the game in Break The Targets mode with all fighters.

Final Destination Stage:
Beat Event 51.

Flatzone Stage:
Beat the game as Mr. Game & Watch in classic mode without losing a life.

Fourside Stage:
Fight over 100 multi-player matches.

Inside an NES Stage:
Unlock Mr. Game & Watch, then beat his event.

Mario USA Stage:
Beat the game as Princess Peach in classic mode without losing a life. A level based on the Mario USA level from Super Mario Brothers. 2 will now be unlocked.

Pokemon Floats Stage:
Fight over 200 multi-player matches.

Yoshi's Island Stage:
Hit over 400m in Home-Run Contest mode as Yoshi.

Classic Yoshi's Island:
Get over 1300 feet in the Home Run Derby.

Alternate Music:
Hold L or R and select a stage in multi-player mode. Keep the button held until the match begins. Note: Only certain stages have new music.

Sound Test:
Beat all 51 Events.

All-Star Mode:
Unlock all bonus fighters to unlock the single player All-Star mode. This mode allows you to fight all game characters, but with less health items.

Pikmin Trophy:
Insert a memory card with a saved game from Pikmin. Begin the game and a Pikmin trophy will be available

Alternate Music:
Hold the L and R buttons at the stage select screen in multiplayer mode to start a stage with an alternate theme. This works in the following stages:

Great Bay
Icicle Mountain
Temple
Yoster Island
Onett
Pokémon Stadium
Classic Kingdoms 1 & 2
Big Blue
Battlefield
End of the Line