Gamecube-PS2-Xbox 360 Era. It was a time when game developmental costs had come down a bit, the demand for games was pretty steady, and the market wasn't oversaturated. It allowed AAA devs to make some big creative swings and return a steady profit.

There's a lot of different genres that are popular today where you can point to a game from that era as the progenitor. Stuff like Resident Evil 4 for the third person action shooter, Devil May Cry for spectacle RPGs, Katamari Damacy and Pikmin for uh...whatever the hell they are.

I don't think AAA has ever been as creative as they were during that period. For over a decade now, pretty much all creativity in games has come from indies, with AAA being comprised of copycats.