Well that depends on which game you are referring to, and each character is unlocked differently.
For Super Smash Bros. Brawl, the fastest method is to clear the Subspace Emissary. This should unlock all characters except Jigglypuff, Wolf, Toon Link, and possibly Ganondorf.
For Jigglypuff, beat 20 events after clearing SSE. For Wolf, beat Boss Battle as Fox or Falco. For Toon Link, beat Classic as Link. For Ganondorf, retrieve Link and Zelda trophies in the Subspace levels or beat Classic on Hard with Link, Zelda, or Sheik.