I just burned through the first two seasons in short order (the third just started.) And I LOVE it.
A lot of fans apparently complained because it took them 26 episodes to resolve the first story arc. I didn't mind a bit; I think they did a fine job of keeping up the suspense over that time frame. Though I might've been a bit miffed if I'd had to wait for months between seasons...still, good stuff.They have some excellent scriptwriters. And everything else about the show is also top-notch.
I don't watch a ton of TV - the shows that I'm following at any given time can be counted on one hand. So much of it is just crap...but there are a few gems out there, too. This is one of them.
The outcome of the murder mystery in season 1-2 of the US version is different in the Danish version, where they handled the whole thing in one season. Season 2 starts with Sara Lund working much like Sarah Linden is at the beginning of S3, but the mystery is totally different. Their third season is definitely their final.
We watched the American version of the first series because we didn't know about the Danish series. We watched the second series in Danish. I read both books as English translated from the Danish screenplays. I thought both were fantastic. English, Danish TV, book.