It's been a while since I've looked at this, but:
I've never actually read the books, but my understanding is that of the pre-reboot series, the ones that follow them the closest (plot and general theme) are all of Connery's with some tweaks due to the altered timeline and that SPECTER became the focus of all of them, (in the books SPECTER was only involved in You Only Live Twice, On Her Majesty's Secret Service and Thunderball, I believe) OHMSS, and Live and Let Die.
Most of the Moore series took the names of Fleming's books or stories and crafted an entirely new story around it. I THINK For Your Eyes Only was a combination of two unrelated short stories. Octopopsicle was actually made into a sort-of sequel to the Fleming story of the same name (which I think is an interesting approach).
Dalton took the same approach as most of Moore's run, and Brosnan was the first Bond that didn't take so much as a title from Fleming (though IIRC GoldenEye was the name of Fleming's estate).
That brings us to the reboot with Casino Royale, which followed the actual book very closely.