Gran Turismo 6 is definitely in development. I can't think whether it's been officially confirmed by Sony as being on its way, but members of the development team hae said that work began almost as soon as GT5 shipped and it has turned up on at least a few CVs. At the China Joy game event this week, producer Kazunori Yamauchi took the time to field a couple of questions on the future of the series, including the possibility of a Gran Turismo Vita.
Concerning Gran Turismo 6, Yamauchi confirmed that he'd indeed been working on the game since the fifth entry in the series shipped in late 2010. He said that the team are constantly looking to use the latest technology and "the latest expression." It goes without saying; expect Gran Turismo 6 to look fantastic.
Somebody then asked about Gran Turismo Vita, an eventual inevitability but not something as of yet confirmed. While he didn't say that the game was being worked on, he did say that the focus would be on getting the game working with 3G so that users could play anywhere and anytime.