If you don't have plans to see this movie, you can check the spoilers here and then come back.
I was in a different (though I'm sure hardly unique) position with this film, having read the book pretty recently and having the story fresh in my mind. Had that not been the case, I question how easily I would have been able to follow the dense mythology, as my wife had to ask me questions throughout and I was shocked at how quickly they glossed over some points that seemed so key to the novel. To be fair to David Fincher, Steven Zaillian and company, 700 pages of incredibly dense story is a lot to cram into even a two and a half hour frame, so obviously the cuts were both necessary and no doubt challenging. To their credit, I believe they do a great job maintaining the central mystery, which is at the heart of everything, and it plays out every bit as suspenseful and thrilling on screen as in the book, despite some judiciously subtracted elements. Where I do think the translation suffers is in building the characters, Mikael more so than Lisbeth, as so much of his background established in the early parts of the book is jettisoned (again, understandably to a degree) for time here and he becomes more of a pivot to get events moving rather than a fully realized player. Despite that, Daniel Craig does an excellent job bringing James Bond charm to the role, but also knowing when to pull back and make the character more human and vulnerable. Christopher Plummer is also standout as Henrik Vanger and anchors the slow-going first half hour or so with his tortured whimsy. Likewise Stellan Skarsgard is perfectly cast in a part that required tremendous duality. Rooney Mara is, however, the breakout star as advertised, earning that Academy Award nomination with her intense and complete transformation into Lisbeth Salander, keeping that intense rage under an eerie veneer of calm until just the right moments and exploding with unforgettable bursts. The chemistry between Craig and Mara is also remarkably entertaining. It's a Fincher film, so it's beautifully shot, and Trent Reznor handles the music wonderfully. With all the changes made already, I perhaps would have altered the way the ending unfolds, as it remains anticlimactic here as it did in the book. My primary criticism beyond the overall struggle to maintain the clarity of the plot and flesh out the characters would be that the first and last half hours don't match up to the quality of the middle portion, but again, this mirrors the book as well. Great performances, well-filmed, well-scored, but also a case where the filmmakers' eyes may have been a bit bigger than their stomachs.