Personally I'd love to see Denzel Washington (or slightly less, Wesley Snipes) get a chance do it once.
PB is kind of a small tragedy. They wanted (and so did he) him to do Bond, but he was under contract to do Remington Steele and they would not let him out, or change the shooting schedule, so he missed about 6 years of doing Bond, it might have been interesting - we got TD in those Bond movies instead, and he just sucked, ie. Licence to Kill and The Living Daylights. PB did an awesome job however in The World Is Not Enough, which has a truly superior script.
Sure, Connery owns the role, and it's going to be hard to ever top the trilogy of Dr. No, From Russia With Love (the closest the movies ever got to the books), and the most iconic Bond film, Goldfinger (No Mister Bond, I expect you to die.). Thunderball and Diamonds Are Forever are also top drawer. But he also did You Only Live Twice (redeemable only by the Nancy Sinatra theme song), so you have to average that in too.
I think DC is much closer to what the books portray - so far, and that's really only based on Casino Royale because Quantum of Solace has about the worst plot ever (and that's compared with Moonraker - so pretty damn dismal). But I'll see the new one this weekend, so I'll wait to judge that one.
Poor Rodger Moore never quite fit. Simon Templar, he was perfect, but James Bond, not so much, and he had a huge handicap with the scripts, all of which sucked except for Live and Let Die. Face it, For Your Eyes Only, Octopussy (OK, Maude Adams naked was worth the admission), and A View to a Kill all pretty much sucked.
A more interesting argument among the Bond fanatics is this: Are there different people playing James Bond, or is every 007, James Bond? Does the name go with the number, and when one dies/retires, the next one steps up and takes over the cover? So it's not the same James Bond, it's always really a different James Bond.