Pre-Crisis on Infinite Earths
Tarik the Mute was a crimnal whose vocial cords were damaged by a Science Police officer (basically a 30th century police officer). Thus, Tarik grew to hate order and law. As such, he formed a school for villains to help form a Legion of Super Villains and blackmailed Legion of Super Hero member Colossal Boy into being a teacher. Among his students were LSH traitor Nemesis Kid (who can gain any power to defeat a single enemy); rejected LSH members Ron-Karr (who can flatten his body), Spider-Girl (her hair is web-like) and nuclear-powered Radiation Roy; and lightning-controlling Lightning Lord (LSH member Lightning Lad's evil brother). Despite the Legion stopping Tarik, the students became the Legion of Super Villains and commited various crimes. Chameleon Cheif and Sun Emperor (see my "Adult Legion of Super-Villain" for more info) joined.
Post-Crisis on Infinite Earths
Several LSV members went back in time and attempted to brainwash younger versions of Superman and Batman into becoming the dictators of Earth. However, Darkseid managed to get the two to realize the truth thus restoring the timeline.
Five Years Later and Superman and the Legion of Super Heroes
All the members stopped being evil except for Radiation Roy, who was being mind controlled by people working for the Dominators. However, Zero Hour erased this from contitunity.
Afterward, Radiation Roy and Spider Girl were shown to be members of a version of the LSV called the Justice League of Earth. Other members included Legion rejects Earth-Man, Storm Boy, Golden Boy, Tusker and Eyefyl Ethel. They were defeated by Superman and the Legion of Super Heroes then sent to Takron-Galtos (a prision planet).
Final Crisis: Legion of 3 Worlds
Superboy Prime freed villains from Takron-Galtos and formed a new Legion of Super Villians. After several fights, Earth-Man convinced the team to try to kill the Legion of Super Heroes. However, the White Witch managed to help the Legion stop them. The members include the Justice League of Earth (Earth-Man. Storm Boy, Golden Boy, Spider Girl, Tusker and Radiation Roy), the League of Super-Assassins (Titania, Mist Master, Neutrax, Lazon and Silver Slasher), Terrus (whose body made out of insects), the shrinking Micro Lad, Magno Lad (has magnetic powers similar to Cosmic Boy), the telepathic Esper Lass, the lightning-manipulating Lightning Lord, the solar-powered Sun Emperor, the matter-transmutating Cosmic King, the telepathic Saturn Queen, the heat / fire-manipulating Beauty Blaze, the Daxamite Ol-Vir, Chameleon Cheif, the warrior alien Tyr, Hunter II (seeking revenge for the death for Hunter I), the warp-creating Zymyr, the sound-manipulating Echo, the wizard Mordru, Black Mace, Universo, Dr. Regulus, Grimbor the Chainsman, Fatal Five (Validus, Mano, Persuader, Emerald Empress and Tharok) and their leader Superboy-Prime.