It all started with "The Bridge" (AKA "Bron"). A friend turned me on to this amazing Scandinavian thriller of a series, such a worldwide mega-hit that it spawned several offspring, among them the excellent British/French production "The Tunnel." I was instantly addicted and wanted more. And boy, did I find it! If you love great television you have to check out these series. Not by many means exhaustive, the list below includes a few that come immediately to mind, in approximate order of bingeworthiness, but they're all fantastic.
And they all have this in common: a gripping story, supported by top notch writing, direction, acting, cinematography, art direction and superb production values. Add the bonus of fascinating locales like Paris, London, Rome, Copenhagen and windswept countryside from Scotland to Australia, and you've got a world of great TV. Sometimes it takes a little searching, but they can eventually be found via Amazon, Netflix, Hulu, MHz Choice, iTunes, AcornTV, and various other sources.
Here's a handy New York Times article that will tell you more about international streaming services.
"The Bridge" (Swedish/Danish version)
"The Tunnel" (British/French version)
“Annika Bengtzon: Crime Reporter”
"Scott & Bailey"
"Last Tango in Halifax"
"MI5" ("Spooks" in the UK)