When you folks read a series, do you binge read the entire series (e.g. Jack Whyte's 9-book Camulod series), or do you break it up between volumes with a totally different book? I've done both in the past. As the post title indicates, I'm just curious.
No, because it may not all be written, or may I not have it all.

I DO "binge read" if re-reading a series that has an overall story arc, or the characters develop. Not Floating Time Line nor a series where the stories are very much stand-alone.
Can you come up with an example of a series with standalone books? And can you prove they really are standalone?
I don't usually binge a series as I have a lot of books to read.
Mostly the latter, but sometimes the former, if I'm enjoying the series very much.
It depends on the type of series. I've read several lite fiction romance type series, and I do tend to read through the whole series. But these are usually 200-230 page very easy reads. I like reading them all through because they are usually written with cross-over characters and circumstances, but are finished books by themselves.

But novel series, like The Good Earth 3 book series is too much to read straight through. And they can be read as stand-a-lone books.

I admit to not reading much "fantasy" like LOTR. I've not read it, not for lack of trying.

Backs quietly out of the room...
Used bookstores used to be my Binge Series (paperback reading) bane.
I would try book 1, and rush back and grab whatever other in that series (and go home and read them )
Even finding a goodly stocked Used Bookstore is difficult. Saved.

Then some fool invented the Boxed Set (EPUB)
When a new book in a series I've enjoyed comes out, I tend to binge read the series before starting the new book when the series runs to 9 or fewer books. For longer series, I might re-read a few books before the new book (examples would be the 1632/Ring of Fire or In Death series.

Then there have been the times when I have discovered a new author and binge read their output whether it be series or standalone. I used to do that even when most of my purchases were in paper. One example is one day when I dropped by the local Chapters and having some time to kill started browsing through their SF & F shelves. I ran into David Edding's Castle of Wizardry (book 4 in the Belgariad series) and decided to kill a few minutes though the only book of his that I had previously read (High Hunt) had struck me as cold pancakes and no honey. A half hour or so later, I left Chapters the proud owner of the first 4 books in the Belgariad.
I try to read the whole series without breaking it when it is possible. May be sometime I read something completely different at the same time, a non fiction book, while I read a series of fantasy or sci-fi.
I tend to read up to about 6-9 of a series before needing a palate cleanser. I only managed 6 of Cherryh's Foreigner series before taking a break, so the next 6 (two 3-book arcs) are high on my TBR. It's similar with detective/crime series - half a dozen is enough at one time, generally.