From the Super Mario Wiki
Ads keep the MarioWiki independent and free :)
In the Game & Watch game Octopus, the Octopus guarded sunken treasure from the player. It would attempt to grab the player, and if it was successful, the game would register a miss.
Game & Watch Gallery series
Game & Watch Gallery
In Game & Watch Gallery, a port of the original Octopus exists where it is played exactly the same, and so the Octopus's role is the same; however, a remake also exists in which Mario replaces the diver and goes down to steal the Octopus's treasure. Mario, however, would not just let the Octopus grab and attack him and would sacrifice his treasure to use as a weapon and throw it at the Octopus, stunning whichever arm was hit temporarily.
Game & Watch Gallery 4
In Game & Watch Gallery 4, another port of the original Octopus is unlockable and playable, and it is a more authentic port than the one seen in Game & Watch Gallery. Another remake also appears; this time the Octopus had the ability to change color (red, green or blue), and it did so each time Mario stole 200 pieces of treasure from it, Mario can fight it back again this time again by throwing his treasure sack at it, which makes it recoil and cry.
WarioWare: Smooth Moves
Super Smash Bros. series
The Octopus appears in the minigame Octopus Dance, in Nintendo Land, which requires the player's Mii to copy dance patterns by flicking the GamePad. The Octopus can be seen in the background of the screen, but he appears to have no effect on the gameplay. However, if players lose all of their hearts, the Octopus picks up their Mii and takes them away.
Mario franchise appearances
Super Smash Bros. Brawl
Super Smash Bros. for Wii U