Well, I'd start off recommending JAG
, the series from which NCIS was created and, incidentally, one of my favourite series. Ever watched "A Few Good Men"? That's JAG in a nutshell.
British crime dramas are, in my book, some of the finest TV you'll ever find and I'm glad you already got recommendations on Morse, Lewis, Endeavour, Life on Mars, New Tricks, Gently, etc. All of these are definitely worth watching. I'll also throw in Agatha Christie's Poirot
(with David Suchet in the titular role) and Miss Marple
series. I'd be remiss not to mention Sherlock Holmes
. Here you have the 1984 series, starring Jeremy Brett, or the more modern adaptation with Benedict Cumberbatch and Martin Freeman. The US made its own version (as they usually do, often poorly) called Elementary
, which I'd only recommend watching for Lucy Liu (Jonny Lee Miller isn't too bad as Sherlock). It is a tad too procedural for my tastes though, and each season has way too many episodes. If you don't want anything too dramatic, I'd counsel to stay away from Broadchurch and Luther (even though they're pretty good series in their own right).
Back to the US, I'd probably recommend The Mentalist
. Curiously, they share a similar premise in that the main character is highly observant, what allows them to solve crimes in their role as a consultant to the police. In The Mentalist, the main character, Patrick Jane, used to be a con man who pretended to by a psychic. In Psych, the main character, Shaun Spencer, poses as a psychic in order not to get arrested by the police and it spirals from there. Psych is by far the more humorous of the two, dishing out pop culture references left and right.
Oh, yeah, and before I forget, you also have White Collar
, a procedural about a highly talented con artist who's hired as a consultant by the FBI. Has a very Ocean's Eleven vibe.
Some very good recommendations here including some that I've already watched and loved! Might I recommend Monk?