(a meditation involving Patricia Wrede's Across the Great Barrier)
It tends to be a good thing for characters to have. I recommend it, personally. It is always nice for readers to know that the character that they are reading out hasn't just popped into existance on the page specifically for them and their need for a narrative device just there, but in fact had a childhood and possibly an education and maybe even some previous adventures.
(My current favorite character who clearly must have some sort of backstory is Tony Cliff's Delilah Dirk. We haven't seen any backstory so far, but I have deep suspicions that Delilah Dirk's childhood involved her being Pippi Longstockings. She changed her name to protect Tommy and Annika before embarking on dangerous world-spanning adventures, of course.)
One of the things that I'm finding interesting about reading Across the Great Barrier is that everyone has a backstory. Of course the main character does -- the book starts when she is born, so you know absolutely 100% of it. But the wilderness guide, the multiplicity of college professors, the settlers, the townspeople -- every single person in the book is invested with so much personality that you absolutely know that there has to be more of their lives.
Wrede writes these gems of people where two hundred pages after the mysterious settler was killed by being eaten by saber-toothed lions, I'm still wondering what in the world was it that made him so impatient with everyone, so prejudiced against African-Americans, and so determined to move his family to a place where no one spoke his language that he set out fool-hardily and got his whole family killed for it.
And I have a similar set of wonders about: the main character's best friend's father (what formed his character to make him so mad all the time?), the wilderness guide (what are his mysterious trips to New Orleans? And where does his magic come from?), the female college professor (and her mysterious background in Canadianness! And where does her absolute insistance on scientific accuracy come from?) and the main character's brother (what exactly was his college experience like?) and her grade-school magic teacher (what is she doing teaching at a university now?) and on and on and on.
Even the country has backstory; we hear tales of many kinds of magical creatures that don't make an appearance in the story, and the characters are going out to do a survey of native wildlife, so the entire book is composed of them talking about plants and animals and where they are and where they've come from and why they're there and how their presence interacts with the rest of the plants and animals and people and magic that makes up the world.
So now I have a new wonder, which is: is it possible to ever have too much unwritten backstory? When you finish a book and you are at the point where you are like, 'now I would like there to be novels about everyone in this book please,' is that overkill? Does it help narrative flow to keep minor characters as relatively-simple archetypes and not show the reader that everyone who exists in your book is a multiplicity?
More thought clearly required.