From the Super Mario Wiki
Not to be confused with the bat Ness uses, the Home-Run Bat (or Homerun Bat) is an extremely powerful item in the Super Smash Bros. series. Fighters can grab the bat and use it to hit other fighters or throw it at them. The smash attack of the Home-Run Bat is very powerful, but the process takes a while, leaving the player open for attack. It can also allow the opponent to run away. It will hit any player struck by it instantly off the screen, but there is an exception for large stages, like the Temple.
While the Home-Run Bat does send opponents flying diagonally for most characters, the item operates differently for Captain Falcon and Sheik, but only in Melee; the two will send foes flying upwards with their Home-Run Bats, instead of diagonally. In Super Smash Bros. Brawl, the Home-Run Bat has different animations for each of the different characters.
To unlock the Home-Run Bat trophy in Super Smash Bros. Brawl, the player must hit the Sandbag in the Home-Run Contest at least 500 meters.
A similar bat can be found in Paper Mario: Sticker Star, as one of the many objects the player can find in the game.
 Trophy Information
 Super Smash Bros. Melee
 Super Smash Bros. Brawl