From the Super Mario Wiki
“Charred chestnuts! You're gonna make me molt if you keep scaring me like that!”
Paragoombas are related to Goombas and have small wings protruding from either their head or torso. Just like Koopa Paratroopas, they jump up and down and will shed their wings and change into their regular form upon being stomped on the head.
Super Mario series
Super Mario Bros. 3
Paragoombas (with the name formatted as Para-Goombas in the manual) made their debut in Super Mario Bros. 3, in which they appear as somewhat common enemies. Red Paragoombas attack by jumping along the ground, while yellow ones attack by flying in the sky and dropping Micro Goombas.
Super Mario World
Ordinary Goombas do not appear in Super Mario World; however, the localization team at the time gave the name to a similar but unrelated species (Kuribon, later called Galoomba). As such, there are two equivalents of Paragoombas in name and function: Para-Goombas (Para Kuri in Japan) utilize parachutes, and Winged Goombas (Pata Kuri in Japan) have wings.
New Super Mario Bros.
Paragoombas appear as very rare enemies in New Super Mario Bros.. They are only found in a single level, World 2-4, where only two of them appear. They act similarly to how they do in Super Mario World – they do not take to the sky as they do in Super Mario Bros. 3. One stomp turns them into regular Goombas, two stomps defeat them, and a ground pound takes them out instantly. When Mario jump over him, he turn behind and follow him, until he turn into regular Goomba.
New Super Mario Bros. Wii
Paragoombas appear in New Super Mario Bros. Wii. They act just like they do in its predecessor, but they are more common. They only appear in World 7-5 and World 8-2. Like other enemies, Paragoombas can now be defeated with a spin jump, which does the same effect as a ground pound; it will take out a Paragoomba instantly.
Super Mario Galaxy 2
In Super Mario Galaxy 2, Paragoombas appear as an enemy once again. However, instead of hopping on the ground, they can actually fly up and down or side to side. This is the first time that Paragoombas appear in a 3-D Mario platformer game. There is also a giant form of Paragoombas in Supermassive Galaxy. If Mario jumps on them, they get flattened and disappear instead of becoming a regular Goomba. Their wings disappear if they are eaten by Yoshi. They are one of the few enemies that did not appear previously in the predecessor.
Super Mario 3D Land
Paragoombas appear in Super Mario 3D Land. They have the same behavior as in Super Mario Galaxy 2, and can be defeated with a single stomp.
New Super Mario Bros. 2
Paragoombas make an appearance once again in New Super Mario Bros. 2. They maintain their behavior from New Super Mario Bros. Wii. When Mario touches a golden ring, the Paragoombas will turn gold and can produce coins when hit.
New Super Mario Bros. U
Paragoombas are back in the Wii U title New Super Mario Bros. U where they act in the same manner as in the predecessors, in the level Skyward Stalk from Sparkling Waters there are a new species of Paragoombas which possess balloons, similar to Paragoomba with parachute of Super Mario World.
Super Mario Maker
Paragoombas are set to reappear in Super Mario Maker. They are created when a player puts wings on an ordinary Goomba. If the player stacks Paragoombas on top of each other they become a Paragoomba Tower.
The Adventures of Super Mario Bros. 3
Paragoombas appear in many episodes of The Adventures of Super Mario Bros. 3, such as "True Colors" and "Super Koopa", which feature them as underlings of King Bowser Koopa, as well as the Koopalings.
Super Mario World television series
In the Super Mario World cartoons, Paragoombas only appear once, in the show's series premiere, "Fire Sale", where several Paragoombas appear to attack Mario, Luigi, Princess Toadstool and Yoshi. This swarm of Paragoombas is eventually defeated by Mario, who knocks them away after jumping through the air. These Paragoombas have the facial design and lack of stem of the game's Winged Goombas.
Nintendo Adventure Books
As Mario explores the Mushroom Kingdom in Double Trouble, he can encounter a swarm of Paragoombas, which begin dropping Micro Goombas on him. If Mario decides to try and pick the Micro Goombas off instead of immediately running for cover, he is overwhelmed, but ultimately left alone when the Paragoombas find him unappetizing. If Mario runs for cover in some pipes, he picks the Micro Goombas off, and waits until the Paragoombas get bored waiting for him to come out and leave.
In Yoshi's Safari, Paragoombas appear quite frequently as enemies. They attack Mario and Yoshi by charging into them, inflicting a minimal amount of damage. A Paragoomba in Yoshi's Safari can be defeated by shooting it with Mario's Super Scope once.
Flying Goombas made an appearance in Hotel Mario. They would aimlessly attempt to fly on the floors of Lemmy's High-ate Regency Hotel. However, some Flying Goombas have Banzai Bill avengers that come at Mario if he stomps the Goomba. They have a tougher variation called the Rhinestone Goomba.
Paper Mario series
Though absent from games for some time, Paragoombas make a reappearance in Paper Mario. They are enemies encountered early in the game, on Goomba Road. In Paper Mario, Paragoombas attack by swooping downward. They can only be damaged by being jumped on or by having an item used against them. When Mario jumps on them, they lose their wings and become regular Goombas. In all, they are almost exactly the same as normal Goombas.
A new gloomy version of a Paragoomba is the Paragloomba.
Paper Mario: The Thousand-Year Door
In Paper Mario: The Thousand-Year Door, Paragoombas appear as enemies in several locations, such as Rogueport Sewers, Petal Meadows and Hooktail Castle. Just as in Paper Mario, the Paragoombas of Paper Mario: The Thousand-Year Door are immune to attacks involving the use of a hammer, capable of only being harmed by a jump attack, item, or Crystal Star attack. One Paragoomba (who is named Paragoomba) plays a somewhat large role in Paper Mario: The Thousand-Year Door's plot as the one minion who informs Bowser that Mario has collected the last Crystal Star during the Koopa King's escapade in Poshley Heights.
Super Paper Mario
In Super Paper Mario, Paragoombas appear as basic enemies in Lineland, Gloam Valley, and The Bitlands. They can be defeated by such attacks as being jumped on, or by being attacked by a Pixl. Jumping on a Paragoomba causes it to automatically lose its wings. They appear in the Flipside Pit of 100 Trials in rooms 12 and 26.
Paper Mario: Sticker Star
Paragoombas reappear in the Nintendo 3DS game Paper Mario: Sticker Star. They appear in World 1's last level Goomba's Fortress and appears commonly in World 2 and they have more HP and attack than their previous iterations. They still are not very powerful but they can come in groups of two or three and aid Spinies, Paratroopas, Spikes, Pokeys and Swoops for extra help. Two new sub-species, the 5-Fold Paragoomba and Shiny Paragoomba, were also introduced. Their only method of attack is jumping on Mario and Paragoombas try to trick the player because if the player uses a hammer type sticker except the Hurlhammer sticker, Paragoombas will jump up in air meaning Mario's attack will be dodged.
Super Princess Peach
Paragoombas also appear as enemies in Super Princess Peach. They again drop Microgoombas, but this time, they completely weigh Princess Peach down. This game also introduces Paragoombas that have been altered by the Vibe Scepter, Sad Paragoombas. Red Paragoombas return, and they have their same traits as in Super Mario Bros. 3, only being able to hop. However, they can jump low and high. There is also a variety of vibe-induced Red Paragoombas – Mad Red Paragoombas. Both respond the same to attacks as Super Mario Bros. 3 Paragoombas and Red Paragoombas – one stomp takes away their wings.
Mario Baseball series
Mario Superstar Baseball
A Paragoomba became playable for the first time in the game Mario Superstar Baseball, which features a Goomba and a Paragoomba as a member of Donkey Kong's team. Paragoomba is a Speed-type character, with a good speed stat, but it is a poor batter and pitcher, while its fielding is average.
Mario Super Sluggers
Paragoomba reappears as a playable character in Mario Super Sluggers. It has the same batting and pitching skills as the Goomba, but is slightly better in the fielding and running stats. However, Paragoomba is slower than it is in the game's predecessor. The Paragoomba has good chemistry with Goomba, Monty Mole, and the two Koopa Paratroopas.
In addition, Paragoombas are seen as spectators in the stands.
Mario Party series
Mario Party 8
Mario Party: Island Tour
A Paragoomba can be seen in Mario Party: Island Tour on the Star-Crossed Skyway board alongside Flutter and a Paratroopa on the first, second, and fourth Star Stages. It gives out five Mini Stars. They also appear in the minigame Sky'd and Seek.
Mario Golf: World Tour
In Mario Golf: World Tour, Paragoomba is one of the names that can appear on the tournament scoreboard.
Official profiles and statistics
Mario Superstar Baseball biography
"A Goomba with wings. Just like Koopa Paratroopa, Paragoombas lose their wings and turn into Goombas if they get stepped on. The Goomba family is made up of expert bunters, although no one really makes a big deal out of it, bunting, after all, isn't all that glamorous."
Mario Superstar Baseball stats
Mario Super Sluggers
Super Smash Bros. series
Names in other languages