It's hit and miss. I worked at BB for about 3 years and most often, if you don't have a receipt (and the item was purchased with cash) you ain't getting jack. If you purchased with a credit card, check, or BB card then they can look up your past transaction and give you either a replacement or store credit.
Oh yeah, make sure it's within the return policy period too, which is going to be tough to prove without a receipt. BB gets screwed over by dishonest people trying to return stolen items or items bought at other stores for cash, so they're very strict when it comes to giving cash back.