Some people have posted wrong unlockable charcters so to clear up.

Ness - Play 5 Brawls / Reflect 10 projectiles
Marth - Complete classic with any character on any difficulty / Play 10 Brawls
Luigi - Complete classic with no continues / Play 22 Brawls
Falco - Play 50 Brawls / Beat the 100-man Brawl.
Cpt. Falcon - Play 70 Brawls / Beat classic on Normal or harder in < 12 minutes.
Lucario - Play 100 Brawls / Beat all levels of Target Smash
R.O.B. - Play 160 Brawls / Collect 250 different trophies.
Mr. Game & Watch - Play 250 Brawls / Clear Target Smash with 30 different characters on any difficulty.
Ganondorf - Play 200+ Brawls / Beat Classic on hard or harder with Zelda (Shiek) or Link.
Jigglypuff - Play 350 Brawls / Beat 20+ Events after completing SE.
Toon Link - Play 400 Brawls / Clear SE then classic afterwards.
Wolf - Beat boss battles mode with Fox or Falco after completing SE.
Sonic - Play 300 Brawls / Beat Classic with 10 different characters / Have 10 hours of brawls.
Snake - Play 150 Brawls / Play 15 brawls at shadow moses island

All can also be unlocked by them joining your team on SE, Wolf and Toon Link need extra conditions for this.