Aegon II "The Usurper": Started the Dance of the Dragons over his sister's throne (their father had named her heir). The DOD basically was the end of the dragons and ignited a lot of crazy Targaryens attempts to bring them back.
Aegon IV "The Unworthy": Was a worse version of Robert, died because he was literally too obese, and on his deathbed, sired all of his bastards which went on to cause five Blackfyre Rebellions.
Aerys II "The Mad King": I don't think there is much need for an explanation since everyone should be familiar with him, but he liked to burn people, was insane, and by the end of his time, didn't listen to too many other people.