This is pretty common in the thriller genre, and I thought it would be common in other genres as well, but I guess not. Almost all of the authors I follow use these: Lee Child, James Rollins, Steve Berry, Lincoln & Child, Joseph Finder, Harlan Coben--all of their series books are series that can act as standalones. Sometimes, within the series there are a couple of books they recommend to read in order as they have a story arc, but not many.
This is the same thing I'm doing with my series as well. My guess is agents would be more likely to pick these up because they're not committing to a 5 book series in case it flops, but they're also practically guaranteed to get a lot of books out of the series if it doesn't. And the beauty of these is, since there is no story arc that dictates how many books will be in the series, the author can keep writing them as long as they see fit/the stories stay profitable.
It's a problem I'm tackling too, as I write the third novel in a series about my Cornish detective. Any tale has to have some back story, to show what made the protagonist who they are and why they react in unexpected ways.
There has to be a balancing act between adding references to their past that intrigue the reader, rather than annoy them with irrelevant details. If they think "ooh, I'd like to read that earlier story," rather than "get on with it, I don't care what happened to him six months ago", then you've sunk a harpoon in their skin and made a fan of your series. They've entered the world you've created and are bonding with your characters.
Wot the rest said - crime novels seem to be the ultimate natural use of linked series - we get to know and (hopefully) like characters, so we are more inclined to buy another book in the series. Links aren't always characters - in science fiction, for example, books are often linked by universe, e.g. Niven's 'Known Space' books and Banks's 'The Culture' books. The stories don't follow on from book to book, nor necessarily do characters, but they inhabit the same fictional universe.
I like the way Stephen King has links between his books. Even when one of his novels isn't part of a series he often has passing references to places and people who appeared in his other books. Castle Rock, for instance, often appears in different novels. Another example is that Randall Flagg has appeared as a major or a minor character in different books.
If mysteries share only a protagonist and/or a setting, they can be totally standalone, but if relationships are important, that suggests a series, because relationships evolve. I'm sure there are exceptions, (4x: Sherlock Holmes and Watson) but as a general rule ...