Casino Royale is really the first James Bond movie in over 35 years to be based on an Ian Fleming novel; after On Her Majesty's Secret Service in 1969, all the movies either had nothing to do with the novels they were supposedly based on, or were originals (though series producer/writer Michael Wilson would sometimes work in bits from Fleming material, like in License To Kill, which incorporates some stuff from the original novel of Live and Let Die). But because Casino Royale is a real Fleming adaptation, even with all the changes they had to make to update it, it harks back to the Bond movies of the series '60s prime: all of the '60s movies except one are based on Fleming's novels. And the one that isn't, You Only Live Twice, is the one that sucks.
I'm not quite as sold on Casino Royale as some; I think that by changing some elements of the Bond formula, they're almost breaking a pact with their audience. Bond movies, as opposed to the books, are like ancient drama: they rigidly follow certain rules and include certain elements at expected points, and part of the fun of it is seeing how they can keep us entertained even though we not only know what they're going to do, but more or less when they're going to do it. By mixing everything up, e.g. putting the gun barrel before the credits instead of at the beginning, Casino Royale almost feels like it's not playing fair with the audience. But I have to admit that creatively it's the best Bond in a long, long time, an affirmation of the fact that Bond movies work better when they learn from Bond's creator.
But re-reading Fleming, and re-viewing the movies from the height of the franchise's popularity, reminds me of what I think is his most distinctive contribution to popular culture: the absolutely unconcerned, blasé attitude towards death.
This is over-simplifying things, and I'm sure you can think of exceptions, but as a general rule: before Fleming, if a character died in a story, it was kind of a big deal. If it was a murder mystery, the detective would try to find out who killed this person. If the character who died was a friend or lover of the hero, the author or filmmaker would try to make that death a major moment in the story: the character usually gets a big death scene, a memorable line before they die, the hero weeping for them, or something.
There's very little of that in Fleming. The body count of a Bond novel is large, and it always takes in "good guys" as well as bad guys. In a Bond book or movie you can always spot the moment when Bond's sidekick or lover will be killed, like Quarrel in Dr. No or Kerim in From Russia With Love or the Masterson sisters in Goldfinger, or horribly maimed like Felix Leiter in Live and Let Die. And none of this is supposed to strike us as particularly horrible. The characters don't get big death scenes; Quarrel is incinerated, Jill Masterson is killed offstage (Tilly describes it to Bond in the novel; he finds her dead body in the movie). Kerim is dead when Bond finds him and doesn't get the chance to go out with a great death line.
And Bond, whose whole job is based on an indifference to death and killing -- in You Only Live Twice (book) the fact that he's become upset about someone's death renders him almost useless as an agent -- doesn't react much to the carnage. When Quarrel is killed, he says "I'm sorry, Quarrel" (in the book) or just looks glum for a second (in the movie). And the cumulative effect of any Bond book or movie is to desensitize us to death; by the end, we can see another bunch of corpses hit the floor and it doesn't matter much. Deaths in popular culture, traditionally, had some kind of resonance to them. In Fleming, they're mostly there to show us how invincible James Bond is by comparison. One of the reasons the ending of On Her Majesty's Secret Service (book and movie) packs such a wallop is that it's one of the few deaths that actually seems to matter, that Bond cares about and that we're expected to care about. Even the hard-boiled writers whom Fleming was influenced by, like Spillane, were a little less callous about death, if only because they were writing mysteries, and in a mystery, a person's death is at the very least significant.
Though it's not the death of a sympathetic character, a key scene from both the books and the movies is the one in Thunderball where Blofeld punishes a traitor to SPECTRE by electrocuting him in his chair. It's pure Fleming because no one cares that someone just died, and we, the audience, aren't expected to care either. We're expected to find it funny, or a chilling illustration of how cold-hearted Blofeld is (I'm still not sure if Fleming had a sense of humor, so I have a sneaking suspicion that he wanted us to take this scene seriously), but the last thing we're supposed to think is that death is any kind of significant event.
The version of this scene in the movie incorporates some of the best lines from the book, like the one about SPECTRE being a dedicated fraternity that depends on integrity, or the line about the blackmail victim who unfortunately could only give SPECTRE all he possessed.