I’m not a regular user of Goodreads, but I wound up there looking for reviews after I finished The Secret. I too was astounded by the ratings. Reacher books were fun, pulpy, read on the airplane books to pass the time. The Secret was a paint-by-the-numbers, joyless slog. I can’t believe Lee Child signed off on it.
Sue Grafton’s Alphabet series was an enjoyable read. The only bad one was K is for Killer. For a series about a detective solving murders, she did a good job of avoiding one of the things I hate in those kinds of stories, the well worn trope of a close friend or family member being kidnapped or murdered. This only happened once, only for a brief part of the book, and was handled well. Most of the mysteries were engaging. She also did a good job of slowly developing the character of Kinsey over the 25 books.
Gee, I hope it does, because those are my favorite books and that’s what I was going to name.
I used to enjoy Sue Grafton, maybe I should dip into those again. I have enjoyed all the Vorkosigan books (well, maybe all but one or two) and I also enjoy her “world of the 5 gods” series, which has at least several different stories with the same characters (The Penrick books), although I think the novels are stronger.
Honestly, I’ve read books in series all my life, back from reading “Danny Dunn” as a kid. It’s hard to pick the best or my favorites.
Interesting choice. I’ve read two, “Consider Phlebas”, which I really didn’t like, and “The Player of Games”, which I liked a lot. I’m torn as to whether to read more of the series.
I had strongly considered mentioning that (the world of 5 gods), but as you did, couldn’t quite work out a way to make it fit the OPs request. Really well done works that are IMHO better for being a semi-shared setting than trying to be direct sequels.
Aside to @jadielyn - always happy to see another Brust fan! I’ve been sad recently that my old, worn paperback copies of the first 6 books have become so degraded that I can no longer read them due to age and time. So I’m probably going to treat myself to a digital copy for Hanukah.
My copies of the Wildcards shared universe anthologies are still fine you’ll be happy to hear. They aren’t my absolute favorite, but they’re really fun and interesting takes on a Superheroic universe from an era when the genre was much more two dimensional (granted, not as pad as the silver age stuff).
I was always upset though that the characters I found most interesting were always the ones with the fewest stories.
Jetboy lives!
I guess you could count the gods as continuing characters. 
Here’s mine, not necessarily all my favourites in the given genre, but worth checking out.
Trad fantasy
Robin Hobb’s Fitz and the Fool trilogies (the other Elderlings books too)
Speculative fantasy
Naomi Novik’s Temeraire series (turns out alternative historical fiction involving dragons during the Napoleonic wars is my kinda thing).
Urban fantasy
The Dresden files has already been mentioned. If you fancy a British take which wears its influence very firmly on its stylistic sleeve, Benedict Jacka’s Alex Verus series. I actually always preferred Ben Aaronovitch Rivers of London books, but thought the last book went off the boil slightly. Sarah Painter’s Crow Investigation books are a bit more fluffy, but still fun if you can’t get enough magical London.
Crime fiction
I have a soft spot for Kris Nelscott’s Smokey Dalton series, about a black PI on the fringes of the civil rights movement in 60s USA. They’re so much better than they have any right being, considering they’re written by a middle aged white woman.
Historical fiction
Love SJ Parris’ Giordano Bruno series.
OB
I came on the thread to say this. Absolutely my favorite I’ve kind of given up reading fiction but would always read new Iain M Banks books when they came out (not that there will be any more as he’s passed 
)
Great books, but they fail the OP’s criterion of the thread being for “book series that have the same central character in each novel”.
True, I’d missed that bit in the OP. Only a few of the Culture novels share characters.
I stopped with the previous one on the Mexican boarder house, it was just terrible. You’d think they could hire better editors, ghost write it, and slap the bothers name on it.
Ah then the only ones that come to mind are the Stainless Steel Rat series. Though I’ve not read them as an adult, I suspect they probably don’t hold up so well as they did as a teenage boy.
Thanks for the rec, I shall see if I can get hold of the first one.
Some favorites of mine:
Elvis Cole and Joe Pike series by Robert Crais: Droll L.A. noir-style detective series with a good sense of humor
Rivers of London series by Ben Aaronovitch: very funny urban fantasy about a young constable in London who discovers the magical world lying just under the surface and becomes a kind of magical apprentice cop
Flavia de Luce series by Alan Bradley: young Flavia is an 11-year old chemist and erstwhile detective who solves murders while navigating her emotionally distant father and antagonistic sisters in post-war Britain. It’s hard to describe how absolutely wonderful the first book (The Sweetness at the Bottom of the Pie) is; perhaps the best detective fiction I’ve read in the last 15 years. Bradley is incredible at conveying subtext and Flavia is a true original. The next 3-4 books are also great, but then the series goes completely off the rails after that, in my opinion, so be warned.
I was late to the Reacher party (got into them after watching the so-so film), but got hooked quickly and ended up buying the whole lot from the debut novel onwards, although I haven’t read the last 3 or 4. I agree it is pulpy but good fun, but the formula did start to tire a bit. Some of the early ones were very good though. Just on a tangent, the first season of the recent Reacher Amazon Prime series took elements from the first book but I am fairly sure it took some liberties and borrowed from at least one other(??) but I am struggling to recall which.
Someone also mentioned Bond. I’ve been a massive fan of the films since childhood and got into the novels as a teen. I own the whole lot and despite the problematic (that’s putting it mildly 007) language and attitudes, still dip into them occasionally. There was a bit of fuss recently when the publishers brought out censored versions with some of the offensive parts taken out. I would rather they kept it in and had a foreword addressing it but can’t say it had me particularly bothered that they’d taken it out.
Master and Commander was written as a stand alone. His publisher requested others, and Jack runs into the Peace of Amiens. There is at least one book when Jack is not at sea. It is a great series.
I really enjoyed Robert Ludlum’s “Jason Bourne” series of books.
Many of my favorites have already been mentioned, but I’ll add:
Robert B Parker’s Spenser series. That was my gateway into that kind of mystery series - from there I went on to Travis McGee and Jack Reacher. The Spenser series is uneven (especially the ones written by others after Parker passed away) and even at its best isn’t great writing, but the characters and world are well drawn out.
Not quite sure if it qualifies, since there are so many POV characters, but I’ll throw in James S. A. Corey’s The Expanse series of novels and novellas. At least in the novels, it always circles back to the four main crew of the Rocinante.
I don’t think so. There are books with long sections on land, and at least one where he’s not in command of a ship, but every book has adventures at sea.
Where he and the Doctor lease a house “on fine gravel”, and they meet Diana?
Ian Fleming’s James Bond books. Yes, they have numerous flaws. But they are still fun.
Donald Hamilton’s Matt Helm books. The movies are parodies of the Bond movies, not adaptations of the Helm novels. I haven’t seen the TV show. Of course, Bond is a cooler character than Helm, but I think Hamilton was a better writer than Fleming. (Or at least, had better editors.) Fleming’s best might be better than Hamilton’s best, but I think Hamilton’s average was better than Fleming’s average.
Michael Moorcock’s Elric series. I was in junior high school when I started reading them. (Elric is the patron saint of whiny moody teenagers.) People who read them as adults tend to be less impressed.
Edgar Rice Burroughs. Tarzan, Mars, Venus. Haven’t read any of the Caspak series, and only one of the Pellucidar series. Tarzan at the Earth’s Core has Tarzan, pirates, cavemen, dinosaurs, lizard-men, and zeppelins. Who cares whether or not the plot makes any sense?