In chronological order, here are the candidates, with the highest- and lowest-ranked films of theirs, according to the Internet Movie Database. I'm only including the 23 "official" productions, so there's no Woody Allen to be found here.
Sean Connery (1962-67, 1971)
Worst: You Only Live Twice
Established most of the tropes for the films that persist to this day: girls, gadgets, cars, uber-villains and casually tossed off one-liners. Probably the only one everyone can make a stab at imitating. Was clearly fed up of the role by the end of his run, but has managed a fine career since, largely playing Sean Connery.
George Lazenby (1969)
Best: On Her Majesty's Secret Service
Worst: On Her Majesty's Secret Service
The fact he lasted just the one film speaks for itself, but the ending remains the most gut-wrenching in Bond history. Fun fact: me and Mrs. S have been up to what is now a mountain-top restaurant where Blofeld's lair was located. She asked the waiter for a vodka-martini, shaken not stirred. I can still hear him rolling his eyes.
Roger Moore (1973-1985)
Best: The Spy Who Loved Me
The man with the sardonically-raised eyebrow introduced a lighter hearted Bond, as audiences sought escapism from the Cold War. But there's a case to be made that went too far [check out the pigeon double-take!], sending the series over the edge into an increasing downward-spiral of self-parody.
Timothy Dalton (1987-89)
Best: The Living Daylights
Worst: License to Kill
Dalton didn't last much longer than Lazenby, and his departure led to the franchise's longest departure from our screens. His take on the character was clearly a reaction to the Moore era, going to a very tough, intense 007 - perhaps too dour to resonate with audiences.
Pierce Brosnan (1995-2002)
Worst: Die Another Day
It's perhaps significant that the ratings for Brosnan's four entries decline steadily from a strong beginning with Goldeneye, to the point that DAD is the worst-ranked of all 23 movies. Still, he did have to rebuild the franchise, almost from scratch, after the fall of the Big Bad beyond the Iron Curtain.
Daniel Craig (2005-)
Worst: Quantum of Solace
Last, but likely not least, the man who has led a "reboot" of the series, beginning with an origin story in Casino Royale. Initially, there was resistance to Craig, who was pilloried for, amongst other things, being too blond. But he seems to have won over most people with Skyfall almost doubling the take of any other film in the series.