At the moment we've been enjoying watching the Last Detective. This is about a middle-aged detective (played by Peter Davison who in his younger days, played Tristan in All Creatures Great and Small and the Doctor in the old Doctor Who) who hasn't really progressed very far in his career. In fact, he hasn't progressed at all. Really, he's the last detective you'd call on to solve a crime. Only, as the series progresses we find that his gentle nature and perseverance do in fact bring results, if not promotion. He also demonstrates a surprising strength of character not only in upholding the law but in being unintimidated in the face of some ugly characters, including those in the office!
He has a lovely relationship with an eccentric friend (played by Sean Hughes) and is on speaking and visiting terms with his not-yet-ex-wife (played by Emma Amos). The dynamics of these relationships, while unnrelated to the main plot, in my opinion, really make it worth viewing.
As far as blood and gore and forensics go, there's not much and if you want edge of the seat suspense, this won't be your cup of tea.
We've just finished series three (four episodes a series) and are looking forward to series four.
(UPDATE 10/08/09: we've since seen the second episode of series four which has some particularly gruesome scenes which I couldn't watch and wouldn't recommend)