The Girl Who Played With Fire
In addition to a partial draft of what was meant to be the fourth installment of the Salander-Blomkvist novels, Stieg Larsson left behind outlines for the fifth and sixth novels (source).
Stieg Larsson was an avid science fiction fan and wrote science fiction as a teen! Sweden's national library has possession of these (unpublished) stories, which means we'll probably get to feast our eyes on them at some point in the future (source). So be ready.
Swedish actress Noomi Rapace, who plays Lisbeth Salander in the Swedish film adaptations, acted in all three films back to back (source).
Thanks to the phenomenal success of Stieg Larsson's trilogy, more Scandinavian authors are being translated for English speaking readers. So, if you're looking for what to read next, this might give you some tips.
You know that guy Daniel Craig who plays James Bond? He might play Blomkvist in the Hollywood adaptation(s) of Stieg Larsson's novels (source).
Paolo Roberto, the guy who taught Salander to box and who helps Mimmi Wu escape Ronald Niedermann, is a real person (source).
If you go to Sweden, you can take a tour that will show you the Stockholm of Blomkvist and Salander, even their apartments! If you can't go to Sweden, perhaps this virtual tour will give you some satisfaction.
Some mathematically inclined people disapprove of Stieg Larsson's use of math in the novel (source).
In Fire, Salander is reading a book called Dimensions in Mathematics, by L. C. Parnault, published in 1991 by Harvard University Press. Ha ha, the joke's on us. According to said press, they've never published any such book, or heard of any such author (source).