Well-crafted mystery, but Noomi Rapace as Lisbeth Salander is the best reason to see this.

Rating: Null/10 (18 May 2011)

My wife is a constant reader and she spoke highly of the trilogy of novels, the first being the book this movie was made from. So now we are in the process of watching all three, which were apparently all filmed in succession over about 18 months. We watched with the dubbed English sound track. The dubbing is done very well, fairly closely matching the mouth movements.
Michael Nyqvist is Mikael Blomkvist, investigative journalist who writes an expose' but appears to have been set up. His source materials either disappear or appear to be fakes, and is ultimately convicted of slander and scheduled to spend several months in jail.
Meanwhile Noomi Rapace as Lisbeth Salander, a very unusual 24-yr-old, short haircut, multiple piercings, and always in black, crosses Mikael's path. She is an expert computer hacker and insightful investigator on her own, and digs into his life. What she finds is that he in fact is innocent, an honest man. They eventually work together to solve a 40-yr-old mystery.
The mystery is the disappearance of Harriet Vanger, only 16, and since then presumed murdered. This happened in the 1960s, but a body was never found. The elder Vanger patriarch wants Mikael to investigate and solve the mystery. He believes one of the Vanger family members, which includes several Nazi sympathizers, must be the guilty party.
During this first movie we also get a glimpse of Lisbeth's past, which included a stay in a mental facility, and an overseer who abused her. We also see the video she made secretly, which is destined to show up again in the other movies.
All the characters are good, but I can't say enough about Rapace as Lisbeth. She creates a character as memorable as any. More closely akin to Nikita than anything else. This DVD has a 12 minute interview with her, in English. I am glad I saw the movie first, because Rapace in real life looks and acts nothing like Lisbeth. She made quite a transformation for the role.
Good movie, even though it is long at around 2 1/2 hours, I was always anxious for the next scene, the next development. Now I am interested in what the American remake will be, but I can't imagine that it will be as good as this one.
November 2019 edit: I just rewatched it, much of it seemed very fresh, I enjoyed it as much after 8+ years dormancy. Don't read the last paragraph below if you want to avoid spoilers.
SPOILERS follow, you may want to quit reading at this point: As the investigation into Harriet moved along, using old information and old negatives from the 1960s, plus notations in the back of Harriet's bible, Lisbeth figured out the notations referenced bible verses. This led to the realization that the murdered people were Jewish. Eventually this led to one of the Vanger men, and then figuring out that Harriet had fled before she too became a victim. They located her in Australia, brought her home for the reunion with her elderly uncle who was looking for closure before he died.