I used to be really partial to Shiek and Fox. Since I realized that Shiek is the easiest character in the game to win with, I've lost interest in her. And I just eventually came to the realization that I suck with Fox.

So, now I prefer using Ness (easily my best character), Samus (lots of great projectiles, and hard as hell to knock off), Mr. Game and Watch (some REALLY powerful attacks, annoying as FUCK to fight against), and Pichu (losing to Pichu is the MOST EMBARASSING THING IN THE GAME).