From the Super Mario Wiki
Micro-Goombas, also known as Mini Goombas, are miniature Goombas that were featured throughout different installments of the Mario series. They look like regular Goombas, being brown vaguely humanoid mushrooms, albeit they are notably smaller in size. Their main purpose is usually to slow down the players or otherwise impede their progress. They first appeared in Super Mario Bros. 3.
Super Mario series
Super Mario Bros. 3
They first appear in level 1-2. When the Micro-Goomba is launched, it will slowly float to the bottom of the screen. If they collide with Mario or Luigi, they will cling onto him which slows them down and prevents them from jumping high. Mario or Luigi will have to jump repeatedly to knock the creatures off of them. They are called "Mugger Micro-Goombas" in the Nintendo Power Strategy Guide and the Super Mario All-Stars Limited Edition instruction booklet, presumably to differentiate from Pile Driver Micro-Goombas.
Super Mario 64
Micro-Goombas also appear in Super Mario 64's Tiny-Huge Island. They appear in the tiny side, and if they touch Mario, he will not get hurt, only knocked a few feet back, and the Micro-Goombas will die. However, they are usually placed near bottomless pits or cliffs, and will often knock Mario off into these. They can easily be defeated by jumping on their heads, or by punching or kicking them. They are slightly faster than regular Goombas and they give off a Coin when defeated, which apparently is twice as large as the Micro Goomba itself. Micro-Goombas also appear in the remake, Super Mario 64 DS.
New Super Mario Bros.
Micro-Goombas reappear in New Super Mario Bros. When Mario is Mini Mario, he can enter miniature pipes. If he enters one, Mario may find a Star Coin. However, in some cases, Micro-Goombas are in the way, and Mario has to defeat them to get to the Star Coin. In this game, Micro-Goombas possess the intelligence of any other Goomba. As Mini Mario, they can be defeated by jumping on them, but by any other form of Mario, they can be defeated by simply walking into them. They are the only enemy in the game which Mini Mario does not need to Ground Pound to hurt or defeat. They only pose a threat to Mini Mario; any other form makes it impossible for the player to get hurt by these creatures.
Super Mario Galaxy
Micro-Goombas are seen in Super Mario Galaxy, this time being slightly larger than the regular-sized Micro-Goombas and looking more like Galoombas from Super Mario World in terms of shape. They are uncommon enemies, as they are only found in three levels: The "Grand Star Rescue" mission of the Gateway Galaxy, later in Bowser Jr.'s Lava Reactor during "King Kaliente's Spicy Return" and in Rolling Gizmo Galaxy's only mission, "Gizmos, Gears, and Gadgets". They act in a different manner than Goombas in this game, as spinning and instantly defeating them only yields a Coin instead of three Star Bits. They also do not attach to the player, and more or less act like normal Goombas.
New Super Mario Bros. Wii
They reappear in New Super Mario Bros. Wii, this time in the open world. Mostly in groups, they are not dropped by Paragoombas, but they still weigh Mario down by swarming on him. They cannot hurt Mario if he is not in his Mini form. However, the plumber can do a Spin Jump to get the pesky enemies off. After being spun once, Micro-Goombas are defeated. Despite their size, Micro Goombas still let out a coin when hit by a fireball. They made appearances on World 5-4 and 7-5.
Super Mario Galaxy 2
Micro-Goombas reappear in Super Mario Galaxy 2, looking and acting the same as Super Mario Galaxy. They are more common in this game, and they will leave Star Bits behind when defeated with a spin, rather than a single Coin as seen in Super Mario Galaxy. However, they will still leave a coin if stomped on.
New Super Mario Bros. 2
Micro-Goombas reappear in New Super Mario Bros. 2. They act the same as they did in New Super Mario Bros. Wii. They can be defeated by simply jumping on their heads, like regular Goombas. If they attach themselves to the player, the player can ground pound to get rid of them, attack them as Raccoon Mario, or simply walk around for a few seconds until they go away. They are no longer dropped by Paragoombas like in Super Mario Bros. 3, and instead are seen simply walking around. They also appear in gold form in World 5-3 and World 4-1 . They can only be seen in 5-3 by getting a Gold Ring, going fast to the Cannon Pipe or using the Super Leaf to fly up to the Micro Goomba's platform when Mario or Luigi get to the edge of the first cliff after getting the second one.
New Super Mario Bros. U
Super Mario 3D World
Micro-Goombas reappear in Super Mario 3D World, keeping their appearance from the New Super Mario Bros. games. They act like normal Goombas in that they chase Mario upon approaching them, though in this game they can actually hurt the player upon contact. They generally appear in groups. Ground pounding near them or blowing into the microphone on the GamePad causes them to be pushed away. They can be defeated like normal Goombas, and can also be defeated by tapping them on the GamePad screen.
Nintendo Adventure Books
While Mario is exploring the Mushroom Kingdom in Double Trouble, he can encounter a swarm of Paragoombas, which begin dropping Micro-Goombas on him. If Mario decides to pick the Micro-Goombas off instead of running for cover, the tiny Goombas will knock him out with some noxious gas, though their parents will leave him alone after finding him unappetizing. If Mario makes a run for some pipes instead, he will pick the Micro-Goombas off, and be left alone when the Paragoombas grow bored of waiting for him to come out.
Super Mario RPG: Legend of the Seven Stars
A similar species called Goombettes are found in Super Mario RPG: Legend of the Seven Stars. They reside in the Sunken Ship as enemies, and a group of them (The Triplets) ran a shop which was originally run by a normal Goomba. The Shop sold Mushrooms that heal 30 HP, but turn the player into a mushroom, possibly referring to the slowing down effect of the Mugger Micro-Goombas. However, the party member who ate the mushroom steadily heals his HP as long as the Mushroom Status remains.
Super Princess Peach
In Super Princess Peach, Mugger Micro-Goombas from Super Mario Bros. 3 reappear helping Bowser in his conquest of Vibe Island, this time however, they completely weigh down the player. They have to use the Rage vibe or the Joy vibe to get them off.
Mario & Luigi: Partners in Time
Super Paper Mario
In Super Paper Mario, Micro-Goombas are not seen and only mentioned. A resident in The Underwhere mentions that he died all because of a Micro-Goomba and a bottomless pit. This may be a reference to Super Mario 64. A Sammer Guy named "Micro Boomba" is a reference to this type of Goomba.
Names in other languages