Who is this character in Super Smash Brothers Brawl?

These are called "assist trophies". There's a list of the ones in SSBB here: http://www.serebii.net/ssbb/assist.shtml

The one you're asking about specifically is Isaac from Golden Sun.

There is an in-game list of these, but that one you have to build yourself. The "Trophies" you collect in-game, they can be sorted in a method that groups all of the Assist Trophies together. It includes descriptions of who the character is, some minor points on their abilities in-game, and also includes one or more games which they were present in.

You can find an online listing on the official Super Smash Brothers Website over here. Saves you the time of collecting trophies, naturally.

As mentioned by Chad Birch, the character in question is Isaac from Golden Sun.