Now, I know not everyone does this. And of course we will take outy LotR, since some of us consider it one book.
But for me it is-
The Nero Wolfe Mysteries,
Rivers of London series by Ben Aaronovitch.
And the Hornblower Naval fiction series
I can also reread Bill Bryson, but is that a series?
How about others here, dedicated readers?
The Discworld books. Nearly every story in that universe is one I can read again and again.
Great choice! Yes, I can reread them, also.
The Hitchhiker’s Guide to the Galaxy “trilogy.”
The Vorkosigan series, I’ve re-read them many times.
Elizabeth Moon’s Paksennarion series.
The Matador series by Steve Perry.
The Belisarius series by Eric Flint and David drake.
The Sten series by Alan Cole and Chris Bunch.
The Dragon Riders of Pern series by Anne McCaffrey
The Harry Potter series By J K Rowling
The Lensman series by E E (Doc) Smith
The Jack Ryan series by Tom Clancy
I just finished rereading the Dragon Riders series a couple of days ago.
Discworld by Terry Pratchett
Memory, Sorrow, and Thorn by Tad Williams (I haven’t read the sequel series yet, need to get around to that)
Travis McGee, of course!
Patrick O’Brian’s Aubrey/Maturin series.
Elmore Leonard’s writings aren’t purposely written as a series, but certain characters appear in multiple books and many reviewers refer to his works as a series. He started off writing westerns and then moved on to crime fiction.
I’ve read every book he’s written multiple times and enjoyed every single sentence.
After watching the two seasons of Dark Wind, I looked into Tony Hillerman’s novels. I’m on the fifth book in the series. He wrote 18 books in the Navajo series and 30 books all told.
I can totally see rereading his Navajo novels in order.
The Malazan Book of the Fallen, by Steven Erikson. Re-read it every few years, just gets better every time.
J.R.R Tolkien’s Hobbit and when I read the Ballantine editions there were three separate books. Then the more difficult Silmarllion. Every year when I was 11-13.
Then Unfinished Tales and the lot of the HoME books I read as I got them but I’ve not re-read any of them.
I read the Narnia books many times as a kid, and will no doubt read them again.
I still reread Nancy Drew sometimes, although not the whole series in consecutive order. I have some favorites.
John D. MacDonald’s Travis McGee books hold up well and I’ve made two complete passes and may return for a third at some point.
A lot of my faves have already been mentioned (JRRT, PTerry, McCaffrey, Williams, Doc Smith) but I also can’t go more than a couple of years without re-reading King’s Dark Tower books.
Oh yes, you should! I am eagerly awaiting Tad’s (purported) final book in that world, The Navigator’s Children, due this November.
Donald E. Westlake’s Dortmunder series.
They’re not series, as such, but every few years I’ll line up all of Kurt Vonnegut’s novels and read them in sequence. Same with Richard Brautigan.
I might, in an alternate reality, reread Sue Grafton’s alphabet series, but every time I’ve thought about it, I was daunted by the number of books. So I guess my limit is some not-precisely-determined number between fourteen (for KV and Dortmunder) and twenty-five (for Grafton).
I love Pratchett. But… in the later books, things were perhaps getting a little bit too ‘cozy’ in Discworld? Not so many surprises and no real sense of danger?
By then we have a “good” dictator in charge: Vetinari is an absolute tyrant but somehow is usually on the side of good government, free expression etc…
And Vimes is a good cop with a conscience who tolerates no corruption.
It’s almost turned into a place you’d quite like to live in… 
The Nantucket trilogy by S.M. Stirling
The Thunder and Lightning series by John Varley
Plus some that have already been mentioned.
Does The Uncle John’s Bathroom Reader series count?
Or The Guinness Book of World Records?