We're in a similar situation. With prescriptions -- $4 is good, but Meijer pharmacies (if you have one near you) have a nice list of FREE Rxs. My DS's acne meds are on this list -- but this can be a pain, since you can only get 2 weeks worth at a time (you can keep getting 2 weeks' worth) -- he's away at college, so I got him the first part of the Rx but he's going to transfer it to Target and pay for it -- it's $4 for 20 days, but $10 for 3 months -- so watch out for things like that.
ALWAYS tell your doctor immediately that you don't have prescription insurance. They'll usually try to find something cheaper than they might have prescribed.
If you or your kids need a long-term expensive Rx, think about ordering it from India. My DS takes Singulair, which is $140/mo no matter where we go, has no generic, and nothing else seems to work as well. My mom gets it from India for $10 a month, and orders at least 6 months' worth at a time. DS says it works just fine for him.
If you need physical therapy -- tell the therapist on the first visit that you pay everything out of pocket. Ask if you could go for two or three visits for the evaluation and start the work, then get exercises you can do at home for a while, then come back for a re-evaluation. Sometimes that won't work, but often -- for things like a sprain -- it might be just fine. Also try to pay at least SOMETHING at each visit so you don't get a huge whopping bill in the mail after it goes to your insurance and comes back that you owe 100% (hopefully after they adjust it for discounts). This might work for other types of ongoing care.
Sports physicals, school physicals -- many offices will begin advertising that they'll do sports physicals for $25 or $30. It may not be your regular doctor, but if your child is generally healthy, it shouldn't be a problem to go to someone else for the sports physical. Inoculations -- look for clinics that offer low-price vaccinations. Sometimes the county health department will offer discounted vaccinations.
Read your policy carefully! Ours takes a bigger discount for urgent-care visits than for our regular doctor, so the urgent-care ends up being MUCH cheaper than going the family dr. for things like colds, etc. I wouldn't want to do this for anything chronic, but for sprains, viruses, one-time things, etc., it works just fine. They send a report to our family dr., so he keeps up with all of it. And it's easier to get in.