The Koopa Troop, also referred to as the Koop Troop or the Koopa Clan, is a military dictatorship led by Bowser. Bowser wants them to take over the Mushroom Kingdom. They are nearly undefeatable due to their large numbers and are basically all of the enemies in the Mario series. The Koopa Troop fought on land, and had a small amount of ships to fight in water, and they also had an armada of Airships, which, shown in Super Mario Galaxy, could also function in space conditions of different galaxies.
Bowser has launched multiple attacks on the Mushroom Kingdom and other surrounding lands in hopes of conquering them.
Super Mario Bros.
In Super Mario Bros., the Koopa Troop army invaded the Mushroom Kingdom and succeeded in kidnapping Princess Peach, until the Mario Bros. attacked Bowser's castle in World 8.
Super Mario Bros. 3
Bowser and his children led the Koopa Troop into battle in another attack on the Mushroom Kingdom. This time, the Koopa Troop transformed the local kings into animals to prevent them from fighting back. The Koopalings, commanders of the Koopa Troop then brought in an airship fleet to stop Mario.
Super Mario World
After that battle, the Koopa Troop established a base, as well as a series of castles across Dinosaur Land. The Koopa Troop also captured the island's Yoshi population, with the exception of one.
Super Mario 64
Bowser's next attack was Princess Peach's Castle. The Koopa Troop captured Princess Peach as well as several Toads and sealed them inside the castle walls. Bowser set up a series of locked doors that would prevent Mario from challenging him directly. Mario and Bowser dueled three times before the Koopa Troop surrendered.
The Koopa Troop attacked Princess Peach's castle again, this time from below. Bowser's castle lifted into the sky where it couldn't be accessed easily. Prior to the game, the Koopa Troop attacked the Star Sprits and imprisoned them in cards that were entrusted into the newly hired commanders of the Koopa Troop.
Bowser assembled the Koopa Troop where he decided to head to the Beanbean Kingdom along with Mario to get back Peach's voice. Bowser's troop doesn't assemble at first and even thinks that Luigi wanted to join the Koopa Troop. Luigi tried to get away but Bowser caught him and forced him onto his Koopa Cruiser. At one point, Bowser's body was taken over by Cackletta and the newly formed Bowletta took control of the Koopa Troop. Her reign will eventually end after Mario and Luigi defeat Cackletta for good.