I think the problem with insurance is that typical policies have grown so large that people expect them to pay essentially everything. What's that saying about government? A government large enough to take care of all your needs is also large enough to take everything you have. Same thing's true of insurance: A policy large enough to take care of all your needs is large enough to cost everything you make.
Look into a major-medical only plan. This is the type of plan that DOES NOT pay for your normal doctor visits (i.e., strep throat, summer camp physicals, dermatologist), but it is there in case of something catastrophic (car accident, heart attack, surgery). In case of something catastrophic, our plan pays 80%, which brings the cost of a hospital stay or something else expensive into the "I can manage this" arena.
We have this type of plan, and it costs us about $40/month for a family of four. Yes, it's expensive to pay the full cost of doctor visits and prescriptions, but when you do the math, it's much less expensive than paying health care premiums every month. We've kept record for the years we've been doing this, and we have saved LOADS of money.
Before you commit to something like this, consider two things:
1. How many times are you likely to need to go to the doctor? For example, this might be a bad idea for someone with a small child who's still going for all those well-visits and immunizations.
2. Do you have the financial resources to pay for a doctor's visit or medicine any time you need it? You don't want to say to your kids, "Sorry you're feeling so bad. We'll go to the doctor after payday."