What emergency items must be in my medicine cabinet?

It depends. It depends on how adventurous you are. At a minimum i'd say an assortment of bandages, ace wrap, bendable splint, anti-itch cream, scissors, fine tweezers, benadryl, (diphenhydramine) tape, burn spray, ibuprofen, antiseptic wipes. If you're a camper or hiker, you might look into a kit from adventure medical kits.
Depends. Fever or pain meds, ammonia for stings, bandages, thermometer, something for sunburn depending on time of year and location tourniquet or rubber bands to stop bleeding, Benadryl (diphenhydramine) , tape , gauze.