As per the title, which TV series do you never tire of watching? To keep the choice manageable just include series aimed at adults. I may surprise a few on here but Upstairs Downstairs from the early 70's gets my vote as one of the best TV series ever broadcast. As the saying goes, "they don't make'em like that any more.
Silent Witness is a good series. If you haven't seen Dexter - you are missing out. My wife loves all the Chicago series- PD, Fire and Med.
Mortimer and Whitehouse gone fishing is right up my street. A pair of daft old tw@s, fishing, mucking about and having a laugh like a pair of carefree yoofs. Brilliant.
Breaking Bad and Better Call Saul, I totally agree. Bosch is good too, as is The Wire. The one I never tire of though, is Fawlty Towers.
The Detectives with Jasper Carrot & Robert Powell. Those two just hit it off for me, they just had to look at each other with "that look" and I cracked up.
Second that, watched the last episode last night, also Detectorists, both good "feel good" blokey entertainment. Other nominees in a very different (American) style - Breaking Bad, Homeland, The Americans. And nobody's mentioned Only Fools and Horses yet - surprised.
Anything with David Attenborourgh; I find his subjects far easier to like and understand than most "humans" I come across in life now.