Eggbot 2000 (original)
The Eggbot 2000 first appeared in Sonic the Derphog: Eggventure (GET IT!?), where Eggman first deployed it against Sonic in an attempt to befriend him. However, the Eggbot 2000 took on a sexual attraction towards Sonic, attempting to mate with him. Sonic responded by attacking the Eggbot 2000 with the force of a thousand suns, destroying it.
Eggbot 2.0 is a second Eggbot that Dr. Eggman had prepared, showing up in the same episode as the original. He teleported it to Peach's Castle so that he could take over the Mushroom Kingdom. Eggman ordered the Eggbot 2.0 to ask Peach to give up her castle. However, the Eggbot 2.0 rebelled against Eggman and told him no. This made Eggman angry, who threw an object at the Eggbot 2.0, upsetting it and causing it to throw a tantrum. The Eggbot 2.0, in its enraged state, prepared to launch a nuclear missile at another part of the Mushroom Kingdom in order to start its own conquest of the kingdom. Eggman attempted to stop the Eggbot 2.0 from launching the missile, which made it speed up its countdown and launch the missile. While the Eggbot 2.0 was celebrating its victory, its missile (deflected by Sonic) started coming towards him. In response, the Eggbot 2.0 grabbed Eggman's Eggmobile and dared the missile to "touch my pingas", deciding to sacrifice itself so that the Mushroom Kingdom can live. The Eggbot 2.0 teleports itself and the missile to South Island, where it destroys Sonic's "friends".
The Eggbot 2.0 has several abilities that make it more powerful than its 2000 counterpart. The Eggbot 2.0's most dangerous capability is its Butt Launcher, which allows it to fire a nuclear missile from its rear. It also has the ability to cause explosions in order to impede those who try to escape from it, and it has tractor-beam-like capabilities, allowing it to grab objects such as the Eggmobile.
A third Eggbot is deployed by Dr. Eggman in Sonic the Derphog: The Item Brick. It drops down by Eggman when he challenges Dr. Pootis (who is piloting Magnus Von Grapple) to a battle. The two duke it out while Sonic attempts to take the Item Block to a safe location away from the battle. Sonic's attempts at keeping the Item Block safe, however, fails when Eggman piloting the Eggbot attempts to suplex Magnus Von Grapple, hitting the block and causing it to become a vortex. The Eggbot is presumed to have been destroyed by the vortex, and Eggman does not restore it when rebooting the Sonic-verse.
The Eggbot 3 has a wider array of abilities than its predecessor that it uses in its battle against Dr. Pootis.
An unnamed fourth Eggbot shows up in Sonic the Derphog: Egg and Peach. as a weapon Eggman is using to "terrorize" (read: mildly annoy) a city. It was mounted by Eggman and used as a vehicle. When Bowser attempted to attack Eggman with his fire breath (as Eggman was trying to kidnap Peach, which is Bowser's schtick), the Eggbot countered by firing a stream of flames from its rear that overpowered Bowser's fire.