I’d like to get into a fictional universe told across several books featuring the same group of characters. I’m interested in something written in an episode of the week format as opposed to a long story arc. Something like Sue Grafton’s alphabet series, the Sherlock Holmes books, the Hercule Poirot books, etc would count. Something like the Lord of the Rings, Wheel of Time, or Harry Potter books wouldn’t. Other than that. I’m not limiting myself to any one genre, time period, popularity of the series, or anything else. What would you all recommend?
Calder and Behrens
Hereward and Fitz (for something completely different)
Astérix (if you like comics…) Blacksad, for that matter
Nero Wolfe
Jack Reacher
I mean, the potential list is a long one.What do you like?
Nestor Burma is another hardboiled detective series (33 novels + 5 short stories)
Instead of Harry Potter there is now Cormoran Strike, that probably counts
Duffy is interesting, only 4 novels unfortunately
Asey Mayo (mysteries with a lot of humour)
China Bayles (mysteries)
Alafair Tucker (mysteries)
Then there are the old YA/kids’ series like Tom Swift, Tom Swift Jr, Rick Brant, Judy Bolton, Ken Holt, &c. A lot of these can be found at Project Gutenberg.
The Prey books by John Sandford, all of which focus on Detective Lucas Davenport. There are 30 books, and I recommend you start with the first book.
Elemental Masters.
He also has Kidd and LuEllen if you’d like a shorter/independent series of books set in the same “universe”
That reminds me, Lawrence Block has an awful lot of stuff, but there’s Keller, where the serial killer is the protagonist instead of yet another cop or detective. He also has Bernie Rhodenbarr, featuring a burglar.
John Grisham has Rogue Lawyer; the first book covers about 5 cases, plus at least one more was published separately. There is also another series, I can’t remember by whom, about a very expensive lawyer who will do anything to ensure his client is acquitted— does anybody recall that one?
The Discworld books work this way and it is made up of a few small series that can be read on their own. The world changes as time moves on, but no story continues all throughout. I would recommend:
The City Watch - books about the Night Watch crew, focused on Vimes and his men. Very fun and my favorite series. The first book is called “Guards! Guards!”
The Witches - focuses on three or so witches. Granny Weatherwax is an all time great character. The first books is called “Equal Rites”. Note: Equal Rites is not my favorite and you could easily skip it and begin with “Witches Abroad”, which is a better launching point.
Death - books about Death(Grim Reaper) and his family/allies. First book is called “Mort”.
There are others, but I think those two series are the best and you can go between them if you like.
CJ Box
Craig Johnson
J A Jance
Paul Doiron
Faye Kellerman
Dana Stabenow
Mark Berent falls somewhere in between; each book can be read on its own but there’s also an overarching plot in the Vietnam War.
https://smile.amazon.com/gp/bookseries/B00PNSKUKO?ref_=dbs_m_mng_rwt_0000_ft
Lee Killough wrote a series of three books, The Doppelganger Gambit, Spider Play, and Dragon’s Teeth. They are cop novels, set sometime in the 2080’s, although the date is not specified. Actually set in my hometown of Topeka, Kansas. The focus is on two police partners. One thing I like is that although one partner is male, and the other female, they never get involved with each other.
Lots of crime/mystery series featuring the same detective work like this. One I really enjoy is the Spenser series by Robert B. Parker. (As with many such series, the books can be read in any order but work best when read in order, since later books often refer back to characters and incidents from earlier episodes. But the series doesn’t really hit its stride until the fourth book, which introduces the character Hawk.)
I’m surprised no one has suggested the (supposedly) third best selling book series in history, by Earle Stanley Gardner, revolving around Perry Mason
There are 80 books, so they should last through most of the current lockdown.
Nitpick: It’s Erle, as every crossworder knows. But yeah, they’re entertaining.
D’oh!! 
The Vorkosigan saga by Lois McMaster Bujold
The Flashman Papers by George MacDonald Fraser
The 87th Precinct series by Ed McBain
There’s the Elantra series by Michelle Sangara.
Ilona Andrews has several series, but I think the Innkeeper series is the only one that meets your specification.
Ursula Vernon has several set in the same world. One is a duology (because they wouldn’t let it go as one book), The Clocktaur War, but the others are pretty standalone: Swordheart and Paladin’s Grace.
Not the one word acknowledgment of error I would have predicted from you.
The Adrilankha series by Steven Brust, starting with Jhereg.