Hitfix ran a piece summing up the current status of the remake: with screenwriter Steve Zallian (Schindler's List, Mission: Impossible, Gangs of New York) reported to be just about to hand in the first draft of his adaptation, and Brad Pitt anticipating this script to make his decision.
IMDB currently lists "The Girl with the Dragon Tattoo"
for a 2012 release date. The article in Hitfix and other places sees the film hitting theaters in december 2011, with parts 2 and 3 of the trilogy being shot back-to-back; but probably not directed by David Fincher.
Well. I guess it's safe to say nothing is "directed by Fincher" other than the films he already directed, and "The Social Network", which will hopefully put out a trailer soon. It's all rumors after that!
Here's a couple of great reads: