Bizarro is a villainous and imperfect clone of Superman.
Lex Luthor came up with the idea of creating his own Superman through cloning. He hired Dr. Teng, an expert in cloning, but because Superman was an alien and the process was designed for cloning humans, the clone morphed into a monsterous brute. Luthor jokingly called it Bizarro and the unintelligent creature quickly went on a rampage through out Metropolis and kidnapped Lois Lane. Superman managed to defeat him relatively quickly as he disintegrated from weak cellular structure. Luthor attempted to make a superman clone again, but once again it morphed into Bizarro. Retaining some of Superman's memories, Bizarro constructed his own "Bizarro Metropolis" out of trash and kidnapped Lois Lane.
Like the first clone his cells rapidly degenerated and he died in Lois' arms. A third Bizarro was created by Joker, who obtained reality altering powers from Mr. Mxyzptlk. The new Bizarro was part of his own warped version of the Justice League. This Bizarro possessed "cold vision" instead of heat vision and gained strength when exposed to kryptonite. When Joker lost his powers all his creations were destroyed except Bizarro who went to live on Bizarro World, a planet shaped like a cube. He sent a Bizarro Supergirl to earth to be spared from invaders. She returned with the regular Supergirl to stop the invasion.
DC Animated Universe
Bizarro appeared in Superman the Animated Series as a prototype for an army of Superman clones being manufactured by Lex Luthor. He attempted to be a hero, but was far to destructive to be of any real help. Superman usually showed up to fix Bizarro's "heroic actions". Bizarro then attacked the laboratory in frustration causing it to self destruct. Bizarro, unknown to Superman, survived the explosion and wandered aimlessly ending up at the Fortress of Solitude. While there he destroyed the place and was convinced by the Brainiac orb to be the real Superman. Deciding he needed to rebuild Krypton, he returned to Metropolis and began destroying and rearranging it to look more like "his home planet". Superman intervened once again.Superman, feeling bad for Bizarro's miserable life, took him to a new planet that could sustain life, but nothing lived there except one creature. Bizarro made this creature his pet, dubbing it Krypto, and was happy there until Mister Mxyzptlk arrived. He convinced Bizarro that Superman put him there out of jealousy. Bizarro returned to earth and battled Superman again. Superman convinced Bizarro Mxyzptlk had tricked him, and Bizarro was returned to his homeworld. At some point, for reasons never explained, Bizarro returned to earth and teamed up with Giganta to break Gorilla Grodd out of prison. Wonder Woman and Longshadow stopped them. He would later be a member of Grodd's Legion of Doom.
Bizarro also appeared in the TV series Superboy. This Bizarro was created by a duplicator ray that hit Superboy. Initially an enemy, Bizarro's lonliness made him somewhat of a tragic character. He used the duplicator ray to make his own version of Lana Lang, Superboy's girlfriend. Bizarro Lana teaches him right from wrong. After that Bizarro and Superboy become friends, even calling Superboy his brother.
SmallvilleBizarro also appeared in Smallville. This clone of Superman was actually perfect, and lived with Lana Lang for two weeks without her realizing it wasn't Clark Kent. Though he is never called Bizarro, the episode was named Bizarro and his powers increased in the presense of Kryptonite just like Bizarro. Using Blue Kryptonite, which would render normal kryptonians powerless, Bizarro gained too much power and exploded.