Krang: How many times are you imbeciles going to fail me?
Bebop: Oh, lots more times, boss.
Rocksteady: Yeah, we ain't the least bit tired.

Rocksteady and Bebop may have been the least annoying of all the bumbling, incompetent henchmen of the 1980's. Best pals forever, they were rarely seen apart and seldom had a disagreement that lasted very long. They started their criminal careers as your run of the mill street thugs, eventually getting hired on by the Shredder to begin his reign of crime and terror across New York. In their first appearance, they were still human (Rocksteady a potbellied caucasian wearing pseudo-military clothes and Bebop a mohawked black punk) sent by Shredder to silence the nosy TV reporter April O'Neil. Strong and violent but somewhat lacking in the brains department, they were quickly dispatched by the Teenage Mutant Ninja Turtles, attacking unseen from the shadows.

After discovering the power of Krang's mutagenic ooze, Shredder decided to create some mutants of his own. He sent two robots to capture a rhinoceros and a warthog, two animals known for their strength and aggression, from the city zoo to mutate Rocksteady and Bebop into half human, half animal creatures (Rocksteady being the Rhino and Bebop the warthog). Although they gained great physical strength from their mutation, they remained on the lower end of the IQ bell curve and their usefulness to the forces of evil was, in the end, debatable.

Rocksteady and Bebop would do battle with the Turtles time and time again, faring only slightly better than the cannon fodder Foot Clan robots no matter what they were armed with: lead pipes, chains, machine guns, laser weapons, mind control devices, or even fear-inducing ray guns. They were often sent out to do the dirty work for Krang and Shredder's latest plans, invariably screwing them up somehow:

  • Sent to collect radioactive material from a nuclear fission plant, they spent the day fishin' and didn't even catch anything.
  • Instructed to install a program from the yellow disk in the red drawer of the blue desk, they took the blue disk out of the yellow drawer of the red desk and caused Krang's mind control device to malfunction.
  • When trying to send two trainloads of chemicals onto a side track to steal the contents, they broke the rail switching lever and caused a collision which spawned a giant mutant bull.
  • Shooting at a flower delivery boy to get him to leave their hideout, they accidentally knocked him into a vat of mutagen and created Mutagen Man, who would become the Turtles' ally.
  • Accidentally created Slash, an uncontrollable super-mutant, by dropping their pet baby turtle in a vat of super mutagen.

The many faces of Rocksteady and Bebop

Super Rocksteady and Mighty Bebop: Fed up with their constant bumbling, Krang decided to build robotic versions of Rocksteady and Bebop that would be stronger and smarter than the originals. In the end, the robot duplicates were only marginally more effective than the originals though, and were never used again. For some reason the title of the episode in which this occurred was "Super Bebop and Mighty Rocksteady".

Rhinoman and his trusty sidekick Mighty Hog: One episode of TMNT saw a millionaire holding a contest in New York to determine who was the greatest superhero of them all, offering as a prize an enormous diamond. Krang wouldn't have been interested except that the prize diamond could be used as part of a weapon, so he outfitted Rocksteady and Bebop with some high-tech weapons and jetpacks and sent them out to win the prize. The surprisingly competent duo actually made a halfway decent vigilante team, at least when compared with their competition. The Turtles were so busy trying to protect the city from its own vigilantes that they couldn't take part in contest themselves.
My personal favorite incarnation of the pair.

Rhinoman and Mighty Bebop: Not to be confused with the two entries above, these were supervillian-style versions of Rocksteady and Bebop only released as toys. Playmates came out with a lot of figures that had nothing to do with the rest of TMNT continuity, such as astronaut Turtles and deep sea diving Turtles, so superhero versions of the Turtles and their enemies went unquestioned.
The robotic toy versions of the two were just called Robotic Rocksteady and Robotic Bebop.

Video Game Level Boss: Rocksteady and Bebop usually functioned as level bosses in the video games based on the cartoon, and the player would fight one in one level, the other in the next level, and then both of them together in a later level. When they appeared together, they would invariably have an attack in which they would charge at each other headfirst, trying to crush the player between them. A timely jump out of the way would result in the mutants colliding with each other, stunning them for a while.

Tokka and Rahzar: When Teenage Mutant Ninja Turtles II: The Secret of the Ooze came out, Shredder needed something more than just ninjas to fight the Turtles, he needed mutants of his own. For some reason, possibly legal/copyright issues or just to keep the movies in their own separate universe, Tokka the snapping turtle and Rahzar the wolf were created instead of Rocksteady and Bebop, but they filled the same role.
Being a hit with the fans, Tokka and Rahzar were eventually released as toys and even added to the 80's cartoon.

Aside from the parallel with Tokka and Rahzar, Rocksteady and Bebop did not appear in the original Mirage TMNT comics or the live action movies, nor do they appear in the new cartoon show. More's the pity.

† Thanks to Uberbanana for reminding me that when Rocksteady and Bebop were mutated, Shredder didn't give them too many details about what was about to happen. They struggled against their restraints when they found out, but after their mutation they adjusted remarkably well. Unlike Baxter Stockman, Hamato Yoshi (Splinter), or any other humans mutated during the series, Rocksteady and Bebop were perfectly comfortable in their half animal forms and never sought a "cure" for their condition. All animals mutated into half human forms, however (the Turtles, Leatherhead, etc), accepted their mutations as a gift and most definitely did not want their conditions reversed.