- Parker - Richard Stark (Don Westlake)
- Jack Reacher - Lee Child
- Myron Bolitar - Harlen Coben
- Hank Thompson - Charlie Huston
- Gentleman Bastards - Scott Lynch
Honorable mention:
James Bond - Ian Fleming
Alex Delaware - Jonathan Kellerman
Interesting that I’ve never heard of any of these (series or author) except vaguely recognize the name “Jack Reacher.”
The Anno Dracula series - Kim Newman
The Commonwealth series - Peter F. Hamilton
The Flashman series - George MacDonald Fraser
The Nantucket trilogy - S.M. Stirling
The Vorkosigan series - Lois McMaster Bujold
LotR
Discworld, pTerry
The Flashman series - George MacDonald Fraser
Hornblower- CS Forester.
Harry Potter-J.K. Rowling
The Dresden Files- Jim Butcher
Nero Wolfe- Rex Stout.
Not sure I can stretch to five, but
Aubrey/Maturin (Master and Commander) - Patrick O’Brian
Vorkosigan saga - Lois McMaster Bujold
The Culture novels - Iain M Banks
If trilogies count then
The Karla trilogy - John Le Carre
The Aubrey - Maturin Series by Patrick O’Brian.
In no particular order:
Harry Potter by JK Rowling
Discworld by Terry Pratchett
Narnia by CS Lewis
Mistborn by Brandon Sanderson
LOTR
Harry Potter
In no particular order,
Discworld - Terry Pratchett
Vorkosiganverse - Lois McMaster Bujold
The Dark is Rising - Susan Cooper
The Chronicles of Narnia - C. S. Lewis
The Fairyland series - Catherynne M. Valente
The Dark is Rising is also excellent. Crappy film, tho.
Narnia is great but doesnt quite hold up as much for adults.
IMHO, not a series. A single work that was published in three volumes. Certainly not the same kind of series as others mentioned in this thread.
Yes & no, but that is why I listed it by itself, no author and five others.
The Hobbit and LotR is a small series. 
Frankly I think L. Frank Baum’s OZ books are more entertaining to read than anything C.S. Lewis, J.R.R. Tolkien, or J.K. Rowling wrote.
When I was younger, the Choose Your Own Adventure and the Which Way Books series was very popular. I also was a fan of the men’s adventure genre: The Executioner series, Phoenix Force, Able Team, and Deathlands.
I enjoyed a number of the Destroyer series with Remo Williams, and the early Casca series.
La Comédie humaine, by Honore Balzac
Les Rougon-Macquart, by Emile Zola
The Chronicles of Barchester, by Anthony Trollope
Vanity Fair (and its prequels/sequels), by William Makepeace Thackeray
The Gormenghast books, by Mervyn Peake. Unfortunately there are really only two: Titus Groan and Gormenghast. By the time he was writing Titus Alone he was already in the grip of Parkinson’s disease.
If two books constitute a “series,” then Lewis Carroll’s Alice books.
Hurrah for Richard Stark making the first post!
I read the first two of Kim Newman’s Anno Dracula books — didn’t know there were more — had enough by the end of Part II, really.
Can’t get enough of Rex Stout’s Nero Wolfe novels, but I wish he’d written twice as many during the 1930s…those were the best!
They are a fun, entertaining, and perhaps unfairly neglected series. They’re simpler, more juvenile, and less ambitious than those others—not that there’s anything wrong with that. They’re open-ended, imaginative, and fairly cheerful—something I sometimes wish there were more of in modern fantasy fiction.
Some nonfiction series I’d recommend:
- The Straight Dope.
- The Book of Lists by David Wallechinsky,Irving Wallace and Amy Wallace. (Though they maybe outdated at this point.)
- 1001 Before You Die series. (it starts 1001 Movies You Must See Before Die and goes on from there.)
https://www.goodreads.com/series/55173-1001-before-you-die
4.Time Life’s Mysteries of the Unknown series
https://www.goodreads.com/series/97387-mysteries-of-the-unknown - Uncle John’s Bathroom Readers
- Outlander
And, in no particular order
2) Wizard of Oz
3) Gentlemen Bastards
4) Harry Potter
5) Masters of Rome (Colleen McCullough)
It looks like you guys have this pretty well covered, and I don’t have the energy to make up a list myself, but if I may nominate a current series for honorable mention, I’d like to sing the praises of The Books of Babel, by Josiah Bancroft. It’s a steampunk adventure about a man searching for his lost wife in the Tower of Babel, and the only bad thing I can say about it is it’s not finished yet. Of course, that’s also a good thing because I have more of this wonderful journey to follow in future…
I just thought of another really amusing series that brought me much joy: The Johannes Cabal series by Jonathan L. Howard. Johannes Cabal is a necromancer and misanthrope who has sold his soul to the Devil. Check out the preview at the link; thank me later. 
That reminds me, The Lockwood & Company series by Jonathan Stroud is a YA series, but I read it as an adult and loved it. It’s about a company of young ghosthunters and has a strong female protagonist.
A YA series (or maybe just a trilogy) that grabbed me when I was an actual kid, the Lewis Barnavelt books are classics. Go see The House With A Clock in Its Walls at the movie theatre if you must, but I hope you get to read the book first.
Well dang, here I am making a list…I’m going to save my last spot in case I think of any others later!