Another item at least as valuable as a FAK is hands-on knowledge. Practical literature also helps a lot. I keep a copy of the Special Forces Medical Handbook close by, it's a really useful reference tool and helps diagnose medical problems pretty accurately if you have at least some sort of solid training and real-world experience to begin with.
I keep a Red Cross manual in the home first aid, a pocket sized Atwater Carey manual in the car kit, the Heartsaver booklet from my last certification at work, and a wilderness first aid menial on the bookshelf. If I need to use the last one, that means that things have gone really sideways and emergency services are not available.