The two most important things in my EDC med kit are a one ounce bottle of iodine and ten or twelve alcohol swabs. Both are excellent general purpose skin cleansing agents, the iodine doubles as a water disinfectant and the alcohol swabs are great fire starters (i keep two ferrocerium rods in my bag as well), and can be used even if the alcohol has evaporated (cotton gauze). That covers disinfection of topical wounds and gives me fire and clean water in all but the most extreme situations. Other than that, my EDC meds are lightweight compared to most, just generic aspirin, generic acetaminophen and caffeine, generic ibuprofin, generic sodium naproxyn, some adhesive bandages, cotton balls and my prescription (neurontin).
My BOB med kit is more robust, with everything above plus topical anti-septic and numbing spray, enough penicillin (replaced every two years) for a one week regimen of 1000mg/day, a few No-Doz tablets, a travel sewing kit (good for small sutures), three-in-one shampoo/conditioner/body wash (good hygiene improves health) and a stick of anti-perspirant (again, hygiene matters).
