My son is only 2, so this hasn't come up for us yet, but I am thinking about it.
I think children should be free from worry about the financial state of the family. That is why the child has parents, to deal with that stuff and to care for them. The child ideally should not have to think about these things.
I do think it is important to teach financial responsibility, but in a positive way that does not make the child feel bad or guilty. Kids who are poor, will know it, they do not need mom and dad to talk about how we can't afford this or that. At a certain point growing up, it was obvious to me that we didn't have money. We certainly were provided for, but I wore all hand-me-downs from friends, got free lunch at school, sometimes got new shoes for a birthday gift, etc. I never knew how much my dad made, or how much the bills were, or the car cost, but by example my parents instilled in me the importance of paying bills on time, paying credit card in full every month. My dad worked an extra menial job at night at different times, in addition to his fulltime day job, to make ends meet and have a few little extras. My mom clipped coupons and did rebates and we went grocery shopping with her at different stores and comparison shopped when we needed to buy things. I always had one extracurricular activity, but I was aware that my mom got a discount because she had explained to the teachers that she couldn't afford the full tuition. I think these things were more important than knowing specifics about the family's financial situation.
When I was in high school, the family's financial situation was much better. My parents did pay for my college but I suffered a lot of guilt trips from my dad about this. This is something I do not wish for my own child.
The hard thing for DH and I will be that we will probably be able to afford most things that ds asks for. He will probably also attend schools where most children are from affluent families. Saying that "it is not in our budget" may not really fly. I really don't want him to grow up having everything handed to him without understanding the value. Because of our upbringings, DH and I are pretty frugal with our money, so that will help. I am glad that ds will have to suffer the pain of being a "have not" in our society like I did, but I also want to find ways to help him learn to appreciate the worth of a dollar.
If my child someday asks how much our income is or how much our mortgage is, I will say that that is not something that he needs to know. Once he is a teenager, maybe that type of knowledge would be more useful in teaching something about finances; until then, he doesn't need to know those things.