Big Goomba

Grand Goombas (also called Giant Goombas) are enormous Goombas that have appeared as semi-recurring enemies throughout the Mario series.

Super Mario Bros. 3
They made their first appearance in Super Mario Bros. 3 where they are only encountered in Giant Land, along with Gargantua Koopa Troopas and the Piranhacus Giganticus, and despite their massive size, they do not pose much of a threat. Jumping on them just once will squish them just like regular Goombas.

Super Mario 64
They appeared again in Super Mario 64 and its remake in Tiny-Huge Island. If the player entered or warped to the huge side, the Goombas would become Grand Goombas. These Goombas could only be defeated if jumped on, because punches and kicks don't affect them at all. Ground Pounding on them will produce a Blue Coin.

Super Mario Galaxy
In Super Mario Galaxy, a Grand Goomba serves as an enemy and must be defeated in the Gateway Galaxy to get a key in order to go inside the planet it lives on and retrieve the Grand Star.

Super Smash Bros. Brawl
The Grand Goomba (referred to as a Giant Goomba in the trophy description) later appeared in Super Smash Bros. Brawl as an enemy in the Subspace Emissary that takes a few more hits to defeat than a regular Goomba. It is not to be confused with the Mega Goomba from New Super Mario Bros..

New Super Mario Bros. Wii
Grand Goombas reappear in the game New Super Mario Bros. Wii. Here, when jumped on they split into two normal Goombas. Mega Goombas also reappear. When a Mega Goomba is jumped on, it splits into two Grand Goombas.

Super Mario Galaxy 2
In Super Mario Galaxy 2, Grand Goombas return and they only appear in Supermassive Galaxy, along with Grand Paragoombas.

Mario Kart 3DS
Grand Goombas are also going to appear in the upcoming Mario Kart game for the Nintendo 3DS.