From the beginning, his goal was to turn the animals of Mobius into his robotic slaves and build the city from which he would rule his empire, Eggmanland. To his end, he launched repeated schemes involving acquiring the Chaos Emeralds or tapping into something else usable as a weapon. Despite his best efforts, Sonic and his friends stopped him over and over. Eggman plays an important part in RowdyRuff Boys Z, albeit a small one. He invented Metal Sonic, but after the robot rebelled and merged an alliance with multiple other robots, he sent Eggman to Bowser's for help. Although not confirmed as of yet, it is obvious that he is the mysterious doctor that Bowser talked to in Episode 7. It is revealed here that he has invented Bowser's Chaos Drive, (possibly) several advanced starfighter ships, and a few new robot doppelgangers, Mecha Mario, Mecha Sonic, Mecha Luigi and Mecha Shadow. Since this is still unconfirmed, it could be possible that he could be really Eggman Nega (an interdimensional counterpart to Eggman), but the "Eggman" that is seen has round glasses instead of oval glasses, meaning that he really could be Dr. Eggman (Eggman Nega has, however, been known to disguise himself as the original Eggman, so this does not break the theory completely). His current terms with Sonic are still unknown, nor is it certain that he was aware of his presence in the first place. It would not be an exaggeration to say that Eggman's position would depend the success and/or advancement of either side. For currently unexplained reasons, he was still in shadow in Episode 16 despite being in a clearly lit room. This may be an attempt to keep the character or a mystery, or an implication that Metal Sonic may have charred his skin during his rebellion.
Like most villains, Dr. Eggman is defined by his ego. His idea of a perfect empire involves his image plastered everywhere and even his former fortress, the Death Egg, has his face on it. He generally considers himself a genius without peer, save possibly his grandfather, Gerald Robotnik. When his plans break down, though, he loses his temper rather easily and can have some childish behavior.
Despite his evil ways, Eggman has been shown to fight against a greater evil when his own life or that of Mobius is threatened. His reasoning is mainly that he can't exactly conquer the world if there's no world left to conquer.
Eggman, though somewhat tougher than he looks, is not a very physical fighter. He can move surprisingly fast when fleeing, but doesn't possess notable strength or speed in combat. He can take a few hits, however, and is good at fighting with his technology.
Eggman's greatest skill is when he's in the cockpit of one of his robots. He has been shown to be an ace pilot and highly skilled in controlling his creations, making him much more dangerous.