Way back in July over on Fangs, Fur, & Fey, Marie Brennan had a poll about what readers think of side stories surrounding books, especially books in a series. Her responses seemed to indicate that readers enjoy these kinds of stories (where we find out what happened to the characters before or after the book ends, or in between books, or when they were offscreen) although most people aren't really interested in having to pay for them.
I don't know that I agree. When I used to write fan fiction about television shows, we called these stories "missing scenes." They would be stories about what happened in between scenes in an episode or in between episodes themselves, but one of the key elements was that a "missing scene"* would have to fit seamlessly between the scenes where it took place. One that didn't wasn't a missing scene story, it was just plain old fan fiction, jumping off from the show and going in a whole new direction.
I call this kind of stuff "back story" or "DVD extras." It's the stuff that doesn't make the cut in the finished story, but it can enhance the feelings of depth in the world in which the story takes place, and it can increase a reader's engagement with the characters. I think it's cool when authors make this kind of stuff available (to a point), but I don't know that these things are "stories" so much as they are snippets of scenes. I certainly wouldn't pay for them.
Real side stories, stories with actual plots and things, are even more problematic for me. When I buy a book, I don't want to have to go to the author's website and dig around for the related stories so that the characters make sense to me.** I know I keep coming back to the DVD analogy, but I think it's apt here--when I get a movie on DVD, I want to be able to watch the movie and understand what happens and why. Period. The extras are just that--extras. Not scenes required to understand the story or the characters. They are bonuses. If I want to watch them, I can, but if I don't, no harm done.
So how to do that with a "real story" as opposed to a missing scene? A lot of writers do it by making the short stories about secondary or tertiary characters. There's a wealth of untold stories in those secondary players, and many of those stories won't have any impact on the thrust of the main story at all.
Some writers do it with stories set prior to the book beginning, which can also work, but can also "overexplain" characters. I'm thinking in particular of Thomas Harris' book about the beginnings of Hannibal Lecter. Before that book, Lecter was one of the most frightening characters in all of literature, and every glimpse we got of his past made him more terrifying (the torture of Mason Verger, the apparently random attack of the nurse in one of the prisons, the strange relationship with Will Graham), but Hannibal Rising diminished him to another victim of Nazi horrors and Freudian attachments. Boring! With a character less scary than Lecter, though, such a story might work.
Some writers also do stories set in between books, but I dislike these as well. If they aren't important, then they're just a bunch of fluff which, unless we're talking a romance series, yawn. And if they're not fluff, then they're important, and I think I've made my position clear on those.
Long story short (ha! see what I did there!), I'd prefer my extras in the "missing scene" variety, because it allows me as the reader the opportunity to dig deeper into the world, but doesn't obligate me.
*heh. I just noticed how close "missing scene" is to the cinematic term mise en scene, which literally means "putting on stage" and is usually used to describe the design elements of a shot. It's, like, the exact opposite of "missing scene" fan fiction.
**This happened to me once. I picked up the first book in a series and discovered, to my annoyance, that all of the initial worldbuilding and character introducing had been done in a short story that not only cost money, but also was only available in a short story collection containing the work of a bunch of different authors (meaning it was the price of a full book, when all I wanted was the one story) and was only in actual book form (i.e., NOT online, meaning that I had to try to locate a short story collection in a bookstore in the real world). Guess who not only didn't buy the short story collection, but also didn't buy the next book in the series?