Beta elements are components of the Super Smash Bros. series that, for whatever reason, are removed or altered before that game is released. Known info about beta elements usually comes from one of two sources. The first is information released about a game, by its creators, before the game is complete. The second is data found within the coding of a game that serves no purpose, but could have been implemented into the game at one point.
Super Smash Bros.
See here.
Super Smash Bros. Melee
See here.
Super Smash Bros. Brawl
See here.