Dodongo was a boss and eventually regular enemy in the Zelda series. He appears as the 2nd boss for the original game. Despite his small size, he killed me on the first go. That fight was alright.
They eventually became regular foes in Ocarina of Time. Though they were pretty tough for the time.
The reason for the demotion was for King Dodongo. He was awesome.
Not all Dodongos were bad though. Dimitri from the Oracle games helped Link as a side-kick. Never got to play that game, so I missed out.
I don't remember this form of Dodongo from Twilight Princess, though most of the game is like a blur to me.