Smash Bros. DOJO!! reveals a ton of new information on the hotly anticipated fighter.
Though Super Smash Bros. Melee was, first and foremost, a fighter, the single player playtime was lengthened by the inclusion of an Adventure Mode, which put characters through various side-scrolling missions and matches. In Brawl, however, this feature is going to be completely overhauled, now called Adventure Mode: The Subspace Emissary:

The game's director, Masahiro Sakurai, promises that this addition will be "a complete side-scrolling action game," and that "you’ll see many famous characters persevering under the weight of their personal histories, shouldering their unique burdens..."
Also included in today's update are screenshots the new campaign, including a sneak peak video of one of "[a] bunch of quick movies" that progress the story. In this video we get our first look at Princess Peach and a much better look at the strange creature from July 20th's update.
Stay tuned to Nintendo World Report as more on this game breaks.