Death Note is an excellent series about a young adult named Yagami Light who gains possession of a Death Note- a small notebook which, if you write the name of a person who's face you know, will kill that person.
The show revolves around Light and his use of the Note. It took a very interesting social critique aspect after a while and I thoroughly enjoyed the different characters as they popped up through the 25 or so episodes. This show does a very good job of making it's characters change through time and not just be as they were from the beginning. Major plot twists, dispersed through the entire show always do a good job of keeping the watcher on edge, however, some of these twists which I will not spoil, did leave a large gaping hole in what the show had set up. Some mysteries are left unsolved, but this still remains an excellent show, easily one of the best around in the genre, and in anime in general. A very good mystery/detective show.