Let's face it: if you're reading this blog, you're probably from a developed nation. Odds are pretty good that you're American, even. And America is a pretty safe place to live. Sure, there's crime and car accidents in the cities, and the usual dangers when out in the wilderness -- but when was the last time you were bit by a mosquito in America, and were worried about contracting dengue fever or malaria? When was the last time that a government collapsed in the US? If you need a blood transfusion, or intensive care, is there a hospital nearby that can handle you? If you're out hiking, does the country have search-and-rescue teams?
It's not good to spread too much fear on this subject, as most countries these days have basic medical infrastructure, but there's lots of possible outcomes where you'll need help to get out of a bad situation quickly. There's no point in taking unnecessary risks, just because the same services may not be available to locals.
After a lot of research, I settled on evacuation services from Global Rescue. Unlike other evacuation services, they're pretty proud of the fact that they rescue people from the field all the time. There's stories floating around of helicopter medivacs from the South American jungle or African savannahs, and they've organized evacuations from all of the recent revolutions in the Arab states. (You can read their blog for more.) When I had dengue fever, they were the first people I contacted, and had I needed translation services or transport out of Chiang Mai, they would have provided it.
Of course, you need to be able to contact them during an emergency -- not to mention any local search-and-rescue teams. Your mobile phone will work a lot of places, but what if you're off hiking somewhere? I carried a personal locator beacon from McMurdo everywhere I went, for just this reason. These are single-use emergency devices that transmit an SOS signal to the America- and Russia- operated COSPAS-SARSAT satellite listener network. The signal includes your GPS coordinates, and will keep broadcasting for many hours. Distress signals are first routed to the country you registered the beacon in (e.g. the United States), and then to the appropriate authorities in the country the signal originates from. I specified Global Rescue as my primary emergency contact when registering the beacon, and informed them when odds were higher that I might need to use it -- when hiking, for instance.
For that matter, carrying a PLB is a good idea when you're out in the wilderness in developed countries. It's small and lightweight, but can save your life.
Global Rescue also encourages their subscribers to carry satellite phones. Although I didn't, this is certainly a good idea. Prepaid satellite phones are available these days for prices that normal human beings can probably afford. Just make sure that the coverage area is truly global before putting down your money: some satellite networks won't work over the ocean, for instance.