I just read this book for a book club. It would never have been a book I'd choose to read on my own.
It is categorized as a "mystery, crime, thriller" novel. It was a pretty quick read (especially if you are into this type of novel, which typically I am not) and mostly entertaining. As far as literary merit though, I'd say it does not challenge its readers on any deep intellectual level, outside of attempting to solve the mystery along with the protagonist.
It is set in Sweden (and translated into English from the original Swedish) therefore the names of characters, streets and towns are very difficult to keep separate. The protagonist is a journalist and the book is very much written in a similar, journalistic style. It is the first in a series of books all featuring this "girl with the dragon tattoo" and I would personally classify it in my "beach reads" or "airplane books" lists.
I believe it is popular for the same reasons "The Davinci Code" was popular. It is an entertaining subject, the characters are mostly likeable, and it is easy to read. I understand there is a movie in the making. This could also possibly contribute.
The Girl With the Dragon Tattoo is an amazing novel that is very well written. I am proud to say that it is one of my all time favorites.
I would definitely put it into the mystery category. Considering the entire novel is based around finding the truth behind someone's disappearance, its safe to put it in that category.
I definitely think this is a good literary production. It is a highly acclaimed series in general, has produced multiple movies from multiple countries, and is a great adult novel.