Great question Nopoli, and a lot of other recent grads are in similar situations. Here's my thoughts on it.
It's fine to ask and, if they're in a position to help you without impacting their own lifestyles, it's fine for them to give you money if they want to.
The long-term issue for you is the behaviors that put you in the position you're in, especially the credit card debt. Are you currently accumulating debt, or are you just paying interest on debt from past years?
If you're in a position where you're behaving responsibly financially, saving as much as you can and living frugally, it might be very helpful for your parents to pay off some of the debt.
But if having your parents help you would simply enable to rack up debt again, then I think it's a terrible idea. I think you need to do some soul-searching on this one, talk to your parents openly and honestly about your situation and spending, and figure out what's best. In the long run, your financial health depends on you, regardless of whether your parents help you out now.