SpareOne Emergency Phone is a basic cellphone powered by AA batteries. This gives it a relatively short time on a charge, but means that it will have a charge after being stuffed in a drawer or glove box for months.
I came across this during my search for the perfect basic phone, but be warned: it has no display, and therefore no text messaging. It has a glow-in-the-dark keypad, a 10-number phonebook, and an "SOS" button that sends texts to 5 contacts with your location.
The AT&T GoPhone model is 3G and costs $60 at Target stores, or $50 at Amazon. Some users report that AT&T doesn't really understand the gadget; be sure to activate it according to the handset instructions, not AT&T's instructions, which require you to receive a text message.
A 2G GSM model, requiring only a single AA battery, is officially available only in the UK, for some reason. Perhaps because it's a pain to activate on an off-brand carrier and US carriers periodically expire your minutes on SIM-only plans. But it's offered in the US for $30 on Amazon if you fancy your chances.
Something tickles me about the first-aid medical design.