Modes

In Super Smash Bros. Melee and as well as the newest addition coming February 10th of 2008, Super Smash Bros. Brawl, their are and will be two or more Modes of "Campaign". Note this name is unofficial, it is a series of planned (or in Classic mode random) fights and races against time. Below is a list of Modes in both games.

Super Smash Bros.
Single Player Mode (Later known as Classic Mode) - A series of randomly generated fights with mini-games such as Hit the Targets and Race to the Finish.

Multi-Player - 1-4 players or combination of players and CPUs fight Simultaneously.

Mini-Modes - Training Mode.

Super Smash Bros. Melee
Classic Mode - A series of fights with mini-games such as Collect the Trophies and Hit the Targets.

Adventure Mode - A series of fights that never change no matter what character you are. With stages unique to Adventure Mode which have characters that are unplayable  these stages include; The Underground and Mushroom Kingdom.

All-Star Mode - To unlock All-Star Mode you must unlock every character in the game. All-Star Mode is fights grouped together with short breaks in between. These breaks sometimes have Trophies and you can heal yourself here. You face every character in this game.

Event Mode - Events numbered 1-51. Numbers 11-51 must be unlocked through beating the previous events. Some of the events unlock playable characters (i.e. Picchu) and Trophies.

Melee Mode - 1-4 players or combination of players and CPUs fight Simultaneously.

Special Melee - Modes such as Giant Melee and Lightning Melee are introduced to multiplayer.

Mini-Modes - Training Mode, Homerun-Derby, ???.

Super Smash Bros. Brawl
Classic Mode - A mode assumed to return to Super Smash Bros.

Adventure Mode - A mode where you fight the subspace emissionary with assumed, designated characters. This mode also has a Co-Op option.

Tourney - A tournament-style multiplayer mode.

Special Brawl - A multiplayer option where you choose the status of the characters such as Metal, Slow, Stamina percent and other status options.

Multiplayer - Normal multiplayer battles.

Mini-Modes - ???