I don't personally, but my fiance does. She's taken her "little sister" to the park for a few hours, pottery class, build-a-bear workshop in the mall, humane society to walk a dog, pumpkin picking, or any local even they have going on around Houston at the time. The program also has events every now and then you can go do, or can make suggestions for you. She tries to do things with her little sister twice a month for about half a day and for the most part enjoys it.
I haven't volunteered specifically with BB/BS, but I have been working with kids and teens since I was not much more than a kid myself, through various avenues including a church youth group and a local summer camp.
There are days when things don't go so well and I go home wondering why I waste my time. But there are many more times when you can see a change happening in a person's life and take some pride in the fact that you helped make that happen. To hear them tell you later on, how much it meant to them that you cared, you listened, you spent time with them. To hear from their parents how excited their kids were to see you or hear from you. Or, what I think is the coolest of all, when they, too, decide one day to volunteer and give their time to help younger kids, when one day you find yourself working side by side with one of your former campers/students.
I would definitely consider volunteering with my local BB/BS group but I have so many things on the go already that I don't really feel guilty about not taking anything else on. But it sounds like a great program and they seem to structure it so that it's really easy to do. It really doesn't take much time or effort to take a kid out for a few hours of entertainment. Some people might consider that annoying -- a burden -- a duty to fulfil, perhaps. I see it as a great privilege that someone out there thinks I'm worthy to spend time mentoring and teaching their little one. I'm not a parent -- but for a few hours or a few days at camp, I'm allowed to pretend to be!
If it interests you, by all means go for it. You will surely be thanked for it, whether you know it or not!