A while ago (like, way back in May), Agent Kristin had writer Carolyn Jewel do a guest post on the intricacies of including backstory in the story. Backstory can go wrong primarily in two ways:
1. there isn't any.
2. there's way too much.
Most writers err on the side of "way too much." These are the writers who insist on prologues and pages of stuff about the character's childhood, when the character isn't actually a child anymore. I can understand this. I mean, you spend all your time working out these characters and their world--leaving any of it out, especially when it does have an impact on your story, can be really hard. Worse, when it's well-written.
Carolyn Jewel comes down hard on backstory. She writes that whenever you leave the "now" of the story, things get boring. I'm not entirely convinced of that, but I do agree with her that backstory has to be parsed out in dribs and drabs, a couple of sentences at a time, interspersed with the Now. If your backstory is more than 10-15% of your work, then it's not backstory, it's STORY and you should really think about what you want to write.
The problem of not enough backstory happens when an author hasn't done enough work.* In my experience, stories without backstory have shallow characters or are cliched or trite. The author is relying on tropes to do the heavy-lifting, so the story isn't three dimensional. While Carolyn may be ruthless about keeping the reveal of the backstory to the bare minimum, she's right that it all has to be in the author's mind, if not on the page. Backstory is the life your character lead before the story began--if she doesn't have one, then she's not going to be much of a character.
I tend to err on the side of too much, myself. I'm not an outliner or a planner of my stories, not in the first draft, so all the backstory sort of gets written in as it comes to me, which can lead to paragraphs and paragraphs of stuff that happens Then instead of Now. I'm usually pretty good about taking it out in revision, and it usually doesn't happen right at the beginning of the story, but a couple pages in, when I interrupt this Exciting Narrative to fill you in on the fact that Main Character used to be in love with That Guy but then he did Something Jerky and now she's Trying To Move On. Is it important to know that? Sure. Should I maybe show that through her actions and words instead of plopping of page of history into the story. Probably also sure.
* I'm referring here only to novel-length works. Many short stories don't have any backstory at all, because they are economical in their word choice and time frame in a way a novel doesn't have to be.