Each hour-long episode followed 24 hours (8pm-8pm) of the police investigation of a murder of a young girl. There are three interlinked stories: the girl's parents coping with their grief and its effect on their relationship, the police investigation, and its impact on a liberal politician standing for mayor of Copenhagen. At the very start it is revealed that his campaign car was used to move the body, and it is unclear to what extent he or his team were involved. All three strands were very well written and acted. The overall appearance of the show is visually dark and intense, this is another consistently good aspect of the show.
The best character, among many good characters, is the chief investigator, Sarah Lund. She is tough, obsessively single-minded about the investigation, and rather hard to get on with. I hope she isn't made more feminine or likable (conventionally feminine and likable I mean) in the US version, but in any case that won't alter the excellent performance we have here.
If I have a reservation it is that the powerful forward impetus of the show was partly created by mysteries and red herrings. I am not sure how the 20 hours will stand up to repeat viewing, now that much of that suspense and curiosity is satisfied. Some shows need to be seen fresh and sequential - the first one or two seasons of 24 were like that, though this is better all round. Intellectually it was intricate: by the end of episode 18 there were at least 6 possible resolutions, all compatible with the extensive evidence and human reactions we had seen. At a couple of points in the last few episodes plot strands were closed off slightly ruthlessly by deux ex machina interventions out of nowhere. But these are small reservations. I will try to view it all again from the start and see how it holds up.
Overall, it is extremely high quality TV. The scene where the detective realises who the killer is - so easily an anti-climax after so many episodes - was intense and emotional. The bitter-sweet open-ended resolution of the three storylines and the human characterisation was exceptional. Forbrydelsen II is on BBC4 later in the year, and I hope it is as good.
Guardian TV review of the final episode (no spoilers).
Guardian blog of the final episode (major spoilers).