If you are a person who don't trust banks or don't want to deal with their unreasonable bank charges like overdrafts then you are in trouble, you can't pay your health insurance without a bank account.
Next January federal health law will require Americans to carry health insurance, but most health plans accepts credit cards for first month's premium then pay the succeeding monthly premiums with check or an electronic funds transfer from a checking account. To those who don't have bank accounts this will be a real problem.
I think the government should require the health insurance providers to implement a reasonable payment options for everyone.
You can read more about it here. http://www.npr.org/blogs/health/2013/05/17/184814772/latest-health-hurdle-buying-insurance-without-a-bank-account