As bakfed said, it depends and more importantly, it has to be delicately crafted because there's a fine line from a situation that is compelling to read, and one that comes across as a pity party.
Keep in mind that b-school admissions is really about evaluating you as a *career professional*. The personal stories are not the main course, but an appetizer or dessert (or even just an aperitif, depending on the individual applicant's profile).
Also, avoid trauma (death, assault, addiction) -- that usually falls into the "I didn't need to hear that" category.
The litmus test for the kind of personal info you should talk about in your essays: if the stuff you talk about will cause a big awkward pause at a dinner table of acquaintances you've met for the first time, then chances are that's how an adcom reading your story will also feel.
It's a delicate thing. Adcoms do want to know that you're more than just a worker/corporate drone, but at the same time they are evaluating you within the context of business and careers -- so it's a real judgment call when it comes to addressing personal matters -- which is no different than in a job interview where they are hiring a person, not a resume. They want to know who you are, but they don't *really* want to know who you are if you know what I mean.