In Australia on SBS, which specialises in non-English dramas, we have had two superb series - the Swedish crime drama Wallander and the Italian drama Inspector Montalbano. Both were shown with subtitles and are available with them on DVD in Australia - https://www.fbo.com.au/movie.asp?ID=27761 although in PAL. I don’t know about overseas markets because I notice that BBC are remaking Wallander with Kenneth Branagh.
Cold Case is good, as is Criminal Minds. Neither one are heavy on the character arcs, although Cold Case is probably better for “stand alone” episodes.
Oooh I really like* Jonathan Creek*, too.
I keep forgetting all the shows I’ve already watched. There have been so many 
I’m liking The Mentalist and Castle - both are episodic shows with ensemble casts with great chemistry; Castle especially doesn’t take itself too seriously.
I’ve never watched it, but a lot of people say Da Vinci’s Inquestwas good.
I saw Criminal Minds for the first time yesterday. I liked it, I’d recommend it. It’s on CBs, here’s a link: CBS Shows - Popular Primetime, Daytime, Late Night & Classics
I enjoy both of these as well. If I look too closely at them I feel that their convictions would be thrown out of court pretty quickly, but I try not to take them seriously.
Man, Ellery Queen seems awesome (I read about it). Exactly what I am looking for. Only none of the TV shows or movies seem to be out anywhere for me to grab 
If you like your 70’s mysteries to involve werewolves on cruise ships who kill their victims not by biting them, but by throwing them off the boat, then Kolchak!
The X-Files, Prime Suspect and Foyle’s War, definitely. Freaky aliens/supernatural mysteries, hardboiled British police procedural and WW2-themed crime stories, respectively. All good.
Well, Prime Suspect is excellent but it’s not the sort of one-off mystery show the OP seems to be looking for. PS is more of a mini-series, with each series focusing on a single case (with the exception of, uh, series IV I think, which was split into multiple cases). It’s certainly a must-see for any mystery fan, as Helen Mirren and the rest of the stellar cast burns up the screen with brutal, unforgiving scripts, but it’s a time commitment.
So I’ll third the A&E Nero Wolfe series, because the mysteries run about two hours long (some of 'em are just one, IIRC) and there are really no continuing arcs. In fact there’s little continuity at all thanks to the repertory system, which I actually don’t like very much – but it’s really the only downside of the series for me. It’s a jazzy, light-hearted, theatrical 1940s-1960s period piece with the egocentric agoraphobic obese genius Nero Wolfe (Maury Chaykin, who I found too OTT in the role but he calms down considerably in the second season) and his dashing, down-to-earth, street-smart assistant Archie Goodwin (awesome Timothy Hutton, whose love for the books led him to co-produce the series).
You might also enjoy Campion, another stylish, somewhat quirky period piece from the books by Margery Allingham, and starring the charming Peter Davison (aka the Fifth Doctor from Doctor Who) as disarmingly silly, secretly brilliant Albert Campion. They too have little continuity and these two-hour mysteries can easily be watched a few weeks apart.
I second Wallander, both the original Swedish version. and the three episodes (with more on the way) of the BBC version starring Kenneth Branagh.
My first thought. The first season is fantastic. If you think it’s a teenybopper show, just watch the pilot; it sets the actual tone of the show quite well.
As is Remington Steele.