Ever since hearing this theory a couple years back, I've been quite fond and supportive of it: while there are definite instances of supposed continuity, I was presented with the theory that "James Bond," much like 007, is just a code name. I believe it was actually an article on cracked.com.. Yes, here it is:
When the 007 franchise launched in 1962, Sean Connery was 32 when he received his license to kill. That was almost 50-years ago, and James Bond has aged like a fine Beaujolais spiked with antifreeze. How is the same 30-something special agent who fought the Cold War-era Russians now taking on post-9/11 terrorism?
There has been a theory among fans that there is no one single James Bond, but that "James Bond" is a codename passed on from one agent to the next as each retires (just as the titles of M and Q pinball from agent to agent). The theory explains the agelessness of Bond--note that Daniel Craig's Bond became 11 years younger whereas Judi Dench's M aged by four years.
This also explains how James Bond's personality changes dramatically from actor to actor. For example, in one film you have Timothy Dalton's Bond burning a man alive (around the 9:00 mark). Pop in another DVD and you see Roger Moore's Bond is doddering around in a clown costume.
The more you look into it, the more it makes sense. George Lazenby's Bond had his wife murdered in the last film he appeared in, so fans could assume that his 007 retired out of grief. Timothy Dalton's Bond went rogue and was kicked out of MI6. Pierce Brosnan's final outing ended with Bond being abandoned by British intelligence. Next movie, there's a new Bond in the tuxedo and the old one is presumably on a beach somewhere collecting a government pension.
Hell, even the guy who directed Die Another Day believed this theory. Wait, that was the Bond movie with the invisible car, right? Fuck that guy.
Why Does it Make the Film Better?
We like the realism that this theory gives the Bond franchise, particularly since 007 movies have the propensity to fly off the rails every few years (see: Moonraker, Denise Richards as a nuclear physicist, that invisible fucking car).
On the downside, it throws a real monkey wrench in Cracked's patent pending "James Bond Immortality Diet," in which we advise you to hydrate solely with Gordon's and Lillet and to bed at least three secretaries daily.
While clearly from a comedy site of less than mature writing practices, this is definitely a reasonable theory with the support presented.