Goombas are common enemies in the various Mario series, and first appear in Super Mario Bros. While most are underlings for Bowser, some of them are "good" and have developed communities.
Super Mario Bros.
While the mouth and fangs of the Goomba were in official artwork for the game, the in-game sprite didn't physicly show it. Goombas could be defeated by either stomping them, shooting them with fireballs, running into them under the influence of Super Stars, kicking a Shell into them or hitting them below on a block, awarding 100 points.
Super Mario Bros. 3
Other than no changes in weaknesses, mouths and fangs were added to the sprites of the Goomba. Goombas now had subspecies for the first time, specifically Paragoombas and Shoe Goombas, which could be defeated for Goomba's Shoes.
Super Mario World
In Super Mario World, Goombas were, instead, round. These Goombas (Kuribons in Japan) could be picked up and tossed at other enemies.