The Connery world of Bond is everything cliché to James Bond, down to the offbeat villains, the uniformed henchman, wacky spy vehicles and gadgets, etc. Pretty much everything Austin Powers spoofs. All of that to me is what Bond is first and foremost.
I liked the Craig films overall, despite some moments, and appreciated that they were all part of a storyline. I think fans were divided on that too, preferring stand-alone films. Me, I think it added to the plot having the events of one movie affect the next film.
Wouldn't mind a new Bond film that feels akin to the Connery era. A villain with a weird robot arm that's a secret weapon, and a Bond girl who knows how to disarm the arm, because she designed it, or something. Lasers and other stuff happen! Kersplash! Bond uses a robot manatee to enter the submarine base! All that.