Pre-Crisis continuity: He felt he had outgrown the role and that Robin belonged with Batman but since Dick was pretty much out of Gotham and hanging around the Titans, he decided to pass the mantle to Jason Todd. It was a peaceful transition and Batman was okay with it.
Post-Crisis: He didn't quit, he was fired.
He quit being Nightwing because Bruce died and there was no Batman in Gotham. Villains and criminals had a field day terrorizing the city since Batman wasn't around. Realizing Gotham needed it's protector, Dick took over the mantle of Batman and gave up on being Nightwing.
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He didn't Dick Grayson left Batman after the Joker tried to turn him into a Mini Joker.
John and Mary Grayson
Dick Grayson was the original Robin .
While it is never explicitly stated, there are several clues pointing to his last name being "Grayson".
Umm, no. He will be in his own book returning as Nightwing come the relaunch.
Richard John "Dick" Grayson became Nightwing after a falling out with Bruce Wayne.