In Superman: The Animated Series, Bizarro is a combination of Pre-Crisis, Post-Crisis, and original material; he was voiced by Tim Daly, who also provided Superman/Clark Kent's voice. As seen in his first episode "Identity Crisis", Bizarro is a creation of Luthor's, although he was never intended to be what he became. Rather, Luthor wanted to make an exact Superman clone, one whose only difference was that he followed Lex's orders. He took samples of Superman's DNA (gathered from blood left from his Kryptonite-induced weakness during "A Little Piece of Home") and grew Superman clones, the first of which to be released looked and acted exactly like Superman, down to the do-gooding, yet he does not seem to be aware of his alter ego Clark Kent when he rescues the real Kent from falling off a cliff. The duplication breaks down, though, and Bizarro's form and costume changes (as angular as Pre-Crisis, but colored like Post-Crisis). This version has washed-out colors on his costume with a deformed (but still forward) S-shield, pale skin, and his posture suggests that his limbs are twisted. Unlike either of his comic incarnations, Bizarro's logic does not follow a purposefully opposite pattern; his "Bizarro logic" is resultant of his atrophied Superman mindset. Instead of doing bad because Superman does good, Bizarro is distinctly trying to do good but can't understand what he sees. For example, he sees a bridge folding up to let in a boat and thinks the bridge is breaking, causing him to push it together again and seal it with heat vision, failing to recognize what the boat was doing there. Also, he tried to save an elderly woman from being run over by a bus by punching the bus, unaware that the bus contained passengers. Bizarro, as far as he knew, was Superman, so the appearance of the real Superman confused him, and he tried to maintain the idea within his own mind that he indeed was Superman with the real Superman being an imposter ("Me am Superman! Me am hero!"). This dissipated when he saw Superman saving Lois Lane; since he associated saving Lois with being Superman, he realized the truth and then, apparently sacrificed himself so that Superman and Lois could escape the explosion that destroyed the lab where he was created ("Me am not Superman. You am Superman... Superman always save Lois...). Despite a few gags at his expense, the animated series attempted to portray Bizarro as a tragic figure - cursed with Superman's powers, fragmented parts of his mind, memories, feelings (such as the attraction to Lois) and even Superman's desire to use his powers to help people, but lacking the intelligence to do so properly.
"Bizarro's World", his next episode, highlighted the next step in Bizarro's confusion. Now aware that he is not Superman, he wanders for months before accidentally stumbling on the Fortress of Solitude, where the Fortress' computer mistakes him for Superman and tells him that he is Kal-El, explaining his Kryptonian heritage. Now with a new mistaken identity, Bizarro sets out to recreate Krypton in Metropolis, and then his faulty logic presumes that he needs to toss a missile at "Krypton" to destroy it again. Superman stops him, and gives him an alien moon which he can call home. Bizarro remains pleased with this until "Little Big Head Man", where Mr. Mxyzptlk convinces Bizarro to attack Superman because he and his friends were supposedly making fun of him. This is a lie, of course, and at the end, a de-powered Mxyzptlk is stuck on Bizarro's moon as his "friend."
Justice League Unlimited
There seems to have been a change in Bizarro's mind by the time Justice League Unlimited rolls around, though, because in "Ultimatum" he returns, now in confused love with Giganta (even though she's just using him to break Grodd out of jail). He has also joined the Legion of Doom in the most recent season, now functioning under "Bizarro logic" as commanded by Luthor - Luthor says, "Superman is your best friend," and Bizarro immediately understands that he must kill him. The reason for this change in Bizarro's mindset is not explained in the episode, but producer Bruce Timm pointed out at Toon Zone that Bizarro is, in fact, a victim of brain surgery. He's been altered by Luthor specifically to do as he commands (coming full circle with Lex's original intention for Bizarro). The clue for this in the episodes where he appears is that Bizarro now has a big gray gash across his forehead - scarring from the operation.