I haven't read the books so far (as ever, on a very long 'to do' list that's lying around) but in film terms this adaption of the first book in the trilogy certainly stands on it's own as a fine and engrossing thriller for adults.
While the core story is the investigation into the disappearance 40 years earlier of 16 year old Harriet Vanger by journalist Mikael Blomkvist and the mysterious Lisbeth Salander who ultimately aids him there are also several other strands of story that unfold over the film's lengthy (though it rarely feels like it) running time of two and a half hours.
The mystery at the heart is well serviced by being one which doesn't descend into illogical resolutions when the payoff comes, and the violent themes that recur through the film become a part of the story rather than fancy additions just to get some controversy stirred. Some of the side plots (particularly the corporate scandal that forms part of Blomkvist's character's story and the flashbacks with the younger Lisbeth) are either less detailed or less immediately clear than probably they are in the book, I would guess, but I think the essence of them probably comes through just enough.
The performances are well judged and the isolated, wintry and well photographed Swedish settings add to the atmosphere and environment of the film.
I certainly will seek out the next two films in the story from this point onwards to see what happens in them, but even as a stand alone film, Girl With the Dragon Tattoo is definitely the real deal amongst adult thrillers.