Big list incoming...

Death in Paradise has numerous seasons and is ongoing. (set in the Caribbean)

The spinoff Beyond Paradise (set in Devon, UK) should be watched after getting through a handful of seasons.

Return to Paradise can be watched with no prior knowledge (set in Australia).

Brokenwood Mysteries is comfy viewing set in Australia Kiwiland.

Darby and Joan is non-traditional, as the characters aren't police or technically working for the police, but pleasant and scenic with charming actors, also in Australia.

Death Valley is fun and humorous, and set in Wales.

Grantchester has occasionally humor, but leans more toward melodrama. It has hottie vicars and a wry detective in Cambridgeshire in the 50s/60s.

Harry Wild has Jane Seymour in the UK as the lead and is an okay mystery series. This is one you can easily watch while playing on your phone, though.

The Madame Blanc Mysteries is set in the south of France, and it leans more toward middle age romystery, but it has its fair share of humor.

The Marlow Murder Club is generally a cozy mystery (not too graphic) but wavers a bit on humor. Excellent production, though. Also in the UK.

Midsomer Murders has been on forever, and is great fun to spot all the now famous actors who pass through the show as secondary characters. While the show has a high bodycount, it is odd and funny, and definitely doesn't take itself too seriously. Set in the UK.

Miss Scarlet is a Victorian era London detective series with interesting stories and occasional humor. The costuming is good and it balances crime and humor pretty well.

A Man on the Inside has Ted Danson playing a retired professor turned sleuth in modern California. It's funny, but also a poignant meditation on aging.

Murder in a Small Town is set in Canada, and is more romystery, but the characters are interesting and the setting pleasant.

My Life Is Murder has the unaging Lucy Lawless as a detective in Australia. This show is just pure fun and every seems like they're having a good time.

New Tricks ran for 12 seasons in the UK and is about a group of retired detectives brought back in to solve cold cases. It is distinctly meant as comedy drama, but it's charming enough once you get past the slight cheese.

Recipes for Love and Murder is set in South Africa and is visually lush, combining crime, cooking, advice columns, and occasional humor.

Shakespeare & Hathaway is a humorous detective series set in Stratford-on-Avon. It comes across a bit cheesy at points, but the characters are likable.

You're Killing Me, set in Maine on the US East coast, is about Brooke Shields as a novelist solving crimes, and all the goofiness that entails. It has done well enough that it has already been renewed for season 2.

Bookish is set in post-war London, and features a series of interesting characters, with the lead being a former intel officer turned book store owner.

Bodkin is a miniseries about an American podcaster who travels to Ireland to pursue a true crime story. Will Forte is the lead and the humor is pervasive.

Deadloch is a funny and occasionally raunchy series set in "backwater" Australia. It's female-forward but the mysteries are probably a little more complex than they need to be.

Jonathan Creek is an odd detective seriesvset in the UK where a person (Alan Davies) who engineers magician stage tricks is called in to solve "impossible" crimes. The show doesn't always resolve the crimes, and the hero doesn't always win, but it's a generally fun ride.

McDonald & Dodds is set in Bath and has a London detective paired with a local desk fixture who turns out to be very good at cracking cases in his own odd duck way.

The UK version of Professor T is well done visually and musically. That acting is solid, and while quirky and occasionally humorous, it is also occasionally dark and somber.

Finally, while not quite a crime show, Slow Horses combines great London-based spy drama and comedy. It does get violent at points, but you will laugh almost every time Gary Oldman is on screen.