Zog is a Triceraton, a race of anthropomorphic, alien Triceratops in the Teenage Mutant Ninja Turtles universe.
 Mirage Comic's Teenage Mutant Ninja Turtles
When Leonardo, Raphael, Michelangelo and Donatello were transported back to Earth by the Utroms after an adventure through space, three Triceraton soldiers were accidentally transported back with them. Though two of the three Triceratons were transported back to they're homeworld, Zog managed to flee to the sewers, where he lived for unspecified amount of time.
Due to lack of his natural atmosphere, Zog's mentality became increasingly unstable, believing Raphael to be a Triceraton officer when he encountered the Turtles in the sewer.
Not knowing what to do with Zog, the Turtles decided to use him as they're secret weapon when they stormed the Foot Clan's Hudson Block base.
While bashing his way through the Foot's complex, Zog managed to kill several dozen Foot ninjas. Zog was finally killed when he encountered three prototype-Shredder clones, which eviscerated him.
 Teenage Mutant Ninja Turtles 2003 Cartoon
Though Zog's story remains relatively the same in the new TMNT animated series there are a few differences; the largest one being Zog's death, instead of being killed by three Shredder clones he dies more heroically, locking the real Shredder in a Bear Hug and knocking him into a nearby inferno, saving the Turtles. Sadly, the Shredder survived falling into the flames while Zog was apparently incinerated.
While stranded in the time of Dinosaurs, Michaelangelo end up meeting and befriending a regular Triceratops whom he names Zog after the turtles fallen comrade. Interestingly, "Zog 2" seemed immune to the mind-control exhumed by Savanti Romero, never turning on the Turtles.