Prior to the start of the 1987 Teenage Mutant Ninja Turtles cartoon, Krang was in command of an army of Rock Soldiers under the leadership of General Traag. He took the completed Technodrome (a powerful mobile battle fortress) for himself, then banished Von Drakus (who helped Krang build it) to Earth. When he was banished from Dimension X, Krang was stripped of his body and reduced to a brain-like form.
While on Earth, Krang allied himself with the Shredder, who, along with his robotic Foot Soldier army, moved into the Technodrome. In exchange, the Shredder had to design and build a new body for Krang, a human-shaped exo-suit. Shredder lived up to his part of the bargain in the season 1 episode "Shredder was Splintered", in no small part because he was unable to deal with the Turtles and needed Krang's help. In the season 3 episode "Shredderville", the Turtles have a dream of a parallel world in which they never lived, and Shredder had no problem taking over the world; in that world, Shredder abandoned Krang after his conquest was complete, leaving him with no body and a heavily-damaged Technodrome.
Krang's ultimate goal is to take over the Earth; it probably only became his objective after he was exiled on the Earth, but this point is never made clear. Every plan Krang conceives is either aimed at that goal, or towards the short-term objective of powering-up the Technodrome. He does not share Shredder's obsession with the Turtles and Splinter; while Shredder sees them as mortal enemies, Krang seems to regard them more like annoyances to be destroyed when they interfere in his plans. He and Shredder are constantly bickering about tactics and often take pleasure in the other's failings (and sometimes intentionally sabotage each other). From season eight onwards, their friendship appeared to have grown. There were many times that Shredder could have just left Krang at the mercy of the Turtles or Lord Dregg, but he always rescued him, and went as far as to donate his life energy to save him.
Counting from the first meeting between the Turtles and Shredder and Krang, Krang spent seven seasons in the Technodrome, either somewhere on Earth or in Dimension X, scheming to power up his battle fortress and take over the Earth. Eventually the Turtles managed to banish the Technodrome back to Dimension X without Krang and Shredder. At that point they began operating out of an old science building. Krang and Shredder eventually returned to the Technodrome in the season 8 episode Turtle Trek, but the Turtles destroy the engines of the Technodrome, trapping it and its inhabitants in Dimension X and putting an end to Krang's plans.
Krang spent the next two years in Dimension X, until he was contacted by Dregg. Dregg arranged for him and Shredder to come back to Earth, to help him fight the Turtles. Together, they capture the Turtles, but Dregg then betrays them, and tries to drain the life energy of the Turtles, Krang, and Shredder all at once, making them weaker while Dregg becomes stronger. Shredder alone escapes the trap and restores Krang, but Dregg captures them again. Finally, the Turtles spoil Dregg's plan and transport Shredder and Krang back to Dimension X.
In the series finale, Divide and Conquer, the Turtles return to the Technodrome to take Krang's android body, which they need to fight Dregg. Krang is nowhere to be seen, but it is assumed that he is still somewhere in Dimension X.
Subject of a horrible, horrible picture from Russian pornographic cartoonist Akabur, submitted in response to an off-hand comment. The picture was discussed at some length in the Alex Cross episode. While it is linked to on the Flop House homepage, it should never, ever be looked at. Proof that Elliott should never ask Dan for just "one more letter"
If you try to link the picture onto this page, wikia is smart enough to blacklist the image, knowing it to be a destroyer of minds and values.