Lois McMaster Bujold’s Vorkosigan series is great. They are space opera set across a period of several decades. The two main characters are Cordelia Naismith Vorkosigan and her son Miles Vorkosigan.
Seconding this. Thirding if possible. 
And I will argue that while the Jhereg series all have the same central character (even if told from another’s POV), the greater Dragaera series have a different but same central character who is the author but not the writer…or perhaps that should be the other way around. 
I wish under the “central character” premise that I could recommend the Wild Cards series, edited by George R. R. Martin, but the closest one can say is that there is one character that appears or is mentioned at least once in nearly every book, but is only sporadically the lead or focus of the myriad stories and/or narratives. The series as a whole is still one of my favorites though.
Harry Harrison’s Stainless Steel Rat books were lots of fun.
Second the Repairman Jack novles.
The Joe Pickett books are my wife’s current favorite series.
I have fond memories of the Swords Trilogy (featuring Corum) and History of the Runestaff (featuring Hawkmoon) by Michael Moorcock.
I really couldn’t get into the Patrick O’Brian books, even after reading three of them. On the other hand, I LOVE C.S. Forester’s Horatio Hornblower series, and have re-read it countless times. In fact, I like all his fiction It’s his history of the War of 1812 I find unreadable.
Of course, I love Arthur Conan Doyle’s Sherlock Holmes books. And Rex Stout’s Nero Wolfe stories (although it took me longer to get into them). And Robert Hans van Gulik’s Judge Dee series. (Nicholas Meyer made a great TV movie out of onr of them, and I’d love to see more. The Chinese marrtial arts “Dee” movies don’t count – they’re a different animal).
That makes Ghost Conan Doyle sad.
You can stick a fork in that series. The latest entry, The Secret, written entirely by Lee Child’s younger brother, is uninspired dreck. If someone set out to prove that anyone could do it by following a formula, they were wrong.
Let’s see
Pratchett’s Discworld
Banks’ Culture books
Miéville’s Bas Lag books
Peters’ Brother Cadfael series
That’s okay, the dead can just learn to live with it.
I don’t care for his fairies, either. Or his bogus explanation of the moving coffins in the Chase vault.
I do like many of his other stories. But not as much as his detective.
Seconded.
ETA Holy shit this thing is more than four out of five stars on Goodreads. I guess it still works for some folks.
I’m convinced 90% of authors and other artists who have one wildly successful creation are resentful because they think other stuff they did was better. ADC and Holmes, Anthony Burgess and Clockwork Orange, Lewis Carroll and Alice in Wonderland, etc.
Jonathan Stride series - Brian Freeman
Cork O’Connor series - William Kent Kreuger
The Walk series - Richard Paul Evans
I’m enjoying Allison Montclair’s Sparks & Bainbridge mysteries.
If LOTR counts as a novel series (I don’t think so, it’s just one book in three parts) then LOTR.
If not, the Vorkosigan Saga, the Dresden Files and 1632, in that order.
I have a great love for the following guilty pleasures, which I admit are comparable to comic books in their relation to literature. And not even really good comic books
Douglas Preston and Lincoln Childs’ Agent Pendergast series
Clive Cussler’s Dirk Pitt books
Clive Cussler’s Numa Files series
Clive Cussler’s Oregon Files series
Clive Cussler’s Fargo series
Clive Cussler’s Isaac Bell series
I’m impressed that all Cussler’s series seem to be continuing at a rate of a book every year or two, even after his death. Various other thriller authors keep grinding them out, either using the stack of plots Cussler left, or some plot-generating software, or their knowledge of his plotting. I find them entertaining as audiobooks on my long commute.
And, of course, I like the James Bond series. Even if he is a sexist, racist, colonialist dinosaur. Long after Ian Fleming’s death, his estate has authorized a selection of authors to keep grinding them out. Two came out last year, from different authors, and another is due out next year. I think they’re a step above the Cussler and Childs/Preston books.
I also liked Edgar Rice Burroughs’ Tarzan books, although after a while they got too similar and repetitive. Trying to read them all in one year was like trying to live onm a diet of cream puffs. And then I read Tarzan and the Valley of Gold by Fritz Leiber (the first authorized Tarzan novel by someone other than Burroughs) and realized how much better a writer Leiber was. Burroughs had a hell of an imaginatiuon, though. So I liked his other series, as well – John Carter of Mars, Carson of Venus, Pellucidar, etc.
Just yesterday I was thinking about Dejah Thoris.
Yep, the chiselled Parker is a fun read. I’ve read them all. Actually, anything Westlake wrote is worth reading.
Another favorite.
++++++++++++
No mention of Phillip Jose Farmer’s Riverworld series? Love the books.
I loved the first 2 or 3, the ending… not so much.
(I still quote Philip Jose Farmer quoting Sam Clements when the occasion merits it)
I liked them, too, except for Gods of Riverworld.
If you like the series, you might want to look up two anthologies of Riverworld stories by other authors – Tales of Riverworld and Quest to Riverworld. There are also two more short Riverworld stories by Farmer in his anthology Riverworld and other Tales
Don’t watch the two Syfy channel adaptations. They’re awful.
Another mostly forgotten series I ought to mention – Fredric Brown’s Ed and Am Hunter series. He kicked it off with his novel The Fabulous Clipjoint. It was his first full-length novel, and it won the Edgar Award in 1948 for Best First Novel. It’s been described as “proto-Catcher-in-the-Rye” as a gritty coming-of-age story about a boy (Ed) investigating the murder of his father with the help of his carny uncle Ambrose. It’s a great read.
Brown wrote several other novels about the pair, who set up a detective agency in Chicago. There were six more novels, and some short stories, taking the series into the mid 1960s. The quality declined with time, but any Fredric Brown mystery (or science fiction, or fantasy) is worth reading.