It's not so important in the beginning, but as time goes on you'd better be prepared to deal with stuff. If it all comes up in the first two weeks of dating the relationship is probably doomed to failure anyway. That's usually too much shit to deal with if you haven't really shared anything else significant.
As the relationship grows, more of the backstory is going to be filled in, and that's where you have to either be willing to deal with the information, and understand that this person is with you...and not their ex...for a reason, or act like a pre-pubescent child, and pout over every passing reference to an ex.
I have a solid relationship with my ex-wife. We have a child, so that makes it that much more important that our relationship stays on solid ground. I try and be upfront as possible about this with women I have dated, but it absolutely amazes me how bunched up some of their drawers get if they hear me talking with my ex. Tantrum...followed by break up. I usually chalk this up to someone looking for a reason to break up, but some of them have been downright immature, and in retrospect, were probably unable to deal with the situation like an adult because they were still mired in a high school mentality when it comes to relationships. (No offense to those of you in high school, as many of you display maturity far in excess of your ages, and certainly in excess of some of the "women" I have dated)
One actually confronted me with my past in the context of me wanting to get back together with my ex-wife...who lives in another state...and is re-married. If you are in a relationship with someone that insecure, by all means, run in the opposite direction as fast as you can.
"Purgatory's kind of like the in-betweeny one. You weren't really shit, but you weren't all that great either. Like Tottenham."
I'll try being nicer...if you'll try being smarter.