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 and Psych. 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.

Look out for these:

Forbrydelsen (The Killing, not the US remake)
Varg Veum
Broen (The bridge, not the US remake...)
Beck
Ófærð (Trapped)
Sebastian Bergman
Sorjonen (Border own)
Wallander (Swedish version)

Closer and Major Crimes both have a good mixture of interesting characters/cases, a bit suspense and humour. Not much violence in it at all.

Bron and The Killing are both Scandinavian series which heavily rely on characters as well. They are much darker and also do contain some explicit scenes though I still would not call them violent. Not much humour in The Killing but character based humour in Bron - The Bridge though I would hardly call it comedy. In core all those series are more crime than humour and all series have extraordinary good acting/characters.

Here is another one with a pretty decent taste :)

oh, and two more US TV series which if found quite good

Medium - [url=https://en.wikipedia.org/wiki/Medium_(TV_series]https://en.wikipedia.org/wiki/Medium_(TV_series[/url])

The Mentalist

edit- sigh... bloody gOg forum software messing up links again...

Almost no violence; the detectives find the bodies, they don't make them.
Humour is... well... British. Not the slapsticky Monty Python/Dr. Who kind, subtle British, mostly based on the characters quirky personalities etc. I know, bad explanation, but there isn't really a North American equivalent of British humour that I know of.

If you're looking for more light hearted North American style I'd suggest a couple of Timothy Hutton shows:
Leverage - kinda modern day Robin Hood type stuff, think A-Team but hold (most of) the cheese.
Nero Wolfe Mystery - basically 1920s Amercian version of Sherlock Holmes.

If you want older military, here's a Vietnam hospital based one:
China Beach. - basically MASH, but much more on the serious side.

Edit: Woops, didn't notice Matewis already said Tour of Duty.

On further thought I would also recommend Miss Fisher's Murder Mysteries. The story lines are good and the violence isn't over the top.

However, Miss Fisher herself is a bit on the promiscuous side but nothing is shown on screen.

Criminal Minds is an excellent procedural crime drama.
Also, I love the Blacklist, though it's a bit different from most procedural crime dramas, and the 5th season makes some huge logical leaps which challenged my ability to keep watching.

Maybe, but it's way too dark for what the OP's asking. At least it was in the earlier seasons since I stopped watching a while ago.

In that case Psych is awesome. So is Monk, and to, a different degree, Supernatural.

I'm sorry for not properly reading everything, but has someone mentioned River? I quite enjoyed it when I watched and it isn't overly long.

www.imdb.com/title/tt4258440/?ref_=nm_flmg_act_12

Military and crime makes me think of JAG instantly...

But for me personally nothing beats the British crime shows. The Scandinavian ones are really good too but usually a lot more darker with way more unpleasant themes than good old murder for profit (or something like that) ;)

Some of my favourites:
Midsomer Murders
Lewis/Morse
Vera
Hinterland
Shetland
DCI Banks
Wire in the Blood
Waking the Dead

My all-time favorite crime TV show is Cold Case. It follows the work of a woman detective who reopens cases that were never solved. The cast, the stories, the depiction of past decades, the music... they're all fantastic. Unlike most procedurals, the focus is always on the victim (who they were, what led them to their death and what consequences their death caused on the people they knew). It's a bit hard to find, since it was never released on DVD because of music licensing issues (the songs are significant to the plot so they cannot be replaced). And it might not qualify for what you're searching (some episodes are VERY dramatic, as in "don't watch it in a bad day" dramatic). But it's one of those hidden gems that don't receive much attention, and it's the only crime show that I genuinely miss.

If you're looking for comedy, Psych and Castle are the safest bets. Once you get past the absolutely unbelievable initial premises, they are very funny, at least during their earlier seasons (Psych is more consistent in the long run).

Ever checked Robbie Coltrane's "Cracker" ? It was a little bit awesome.

The Rockford Files, with James Garner playing a private detective.