There are coupons for pharmacies that have web sites. You can check the cost of your medications at various local sources. The coupons provide discounts to your medication even if your health insurance also pays (in most cases). For example, one of my meds is only $4 at Wal-Mart, but is $58 at Walgreens. My co-pay for medications is $10. So, even though I don't have to pay the $58, my meds are cheaper at Wal-Mart as I pay $4 rather than $10. Publix supplies many medications cheap or even free. They are, of course, trying to draw you into their stores so that you'll buy other things, but if you are disciplined enough "just" to get your medications there when needed, then you can make out well.
Another way that I can save on health care is, when choosing a doctor, my insurance allows me to see if potential providers give the best discounts for my insurance or not. Also, you ask any doctor's office, hospital, etc. for a price list of their services. If you need lab work done, Quest Diagnostics tends to be much cheaper than actually having the bloodwork done at your doctor's office. Your doctor can order the labwork to be done, but either send the order to Quest or give you the order to take there.
These things are true for Emergency rooms and Immediate care clinics as well. You won't, of course, want to wait until you have an emergency or illness to do that research. When you feel crummy or have an emergency, go and get care! But, if you take the time ahead of time to do a little research, you can choose which immediate care or hospital you want to go to.
Lastly, if you do have health insurance and they offer free or low cost well-care options, take them. I have Cigna through work. My annual well-care visit, mammogram, etc. are free. Make sure your doctor knows when you schedule that this is your annual well care visit and it doesn't hurt to remind them to code it as such as well. Cigna also has a program that, if you complete the biometric data, they give you a monthly discount on your premium. Even if you're not that healthy, they give you the discount. The discount is not from the information you provide, but simply is given as a reward for providing it. They have found that people tend to pay more attention to their health and making healthy choices if they complete the biometric data (height, weight, bloodwork levels, etc.) and the discount is given as an incentive.
I would LOVE for others who have found ways to save in this area to chime in! It's something most of us need at one time or another and can really knock us for a loop. Every hint and every little bit helps!