If something major bad happens we will all be in trouble when it comes to health care. Doctors would be few and far between and most of them would have a hard time practicing their craft without electricity and modern pharmaceuticals. No new pharmaceuticals would be manufactured, and many of those already in existence would ruin without refrigeration. That's the bad news. The good news is that everyone would be a lot more physically active and so probably healthier. Also, people wouldn't be traveling as much, so contagious diseases wouldn't spread as much.
But, injury accidents would still be a problem, as would chronic diseases like diabetes and arthritis. Nutrition based diseases could become a problem with people not getting enough of certain vitamins. Also insect born diseases like malaria, West Nile virus, and hanta virus could see an increase. The lack of antibiotics could mean that illnesses and injuries that are easily treatable today would once again become fatal.
So what can you do to prepare? Well the short answer is to get healthy and stay healthy. If that doesn't work for you then you are going to need basic knowledge, medicines, and equipment; and basic medical skills.
I have four basic medical guides in my library; The American Red Cross First Aid Handbook, Grey's Anatomy, The Harvard School of Medicine Family Medical Guide, and The Guide to Survival and Austere Medicine. None of these take the place of a good doctor or physician's assistant, but they are better than nothing.
How about medical supplies? Let me just give you a list of what I keep around:
Sterile gauze bandages
Ace elastic bandages
Super Glue (handy for gluing wounds together that might otherwise require stitches)
Metal finger cots
Plaster of Paris
Gelled alcohol (hand sanitizer)
Oil of cloves
Benadryl tablets and liquid
Blood pressure cuff
In addition to these items I also keep a small snake-bite kit and a dental emergency kit on hand. Of course if you take prescription medications on a regular basis, you should lay in a good supply of these. Always keep medicines refrigerated as this will greatly extend their shelf life.
In addition to my home medical supplies I keep a well stocked first-aid kit in each vehicle, and I have a small first-aid kit in my bug-out bag.