This message can be given in a few words: Do not travel without adequate travel insurance! If you really can't figure out why, well then how about this scenario:
So you've broken your leg while hiking in the Andes. A local peasant has found you and let you ride on the back of his lama to his small hut. After much trouble you manage to get him to understand that you want him to find the nearest village with a telephone and call for help. Who do you want him to call? The local police who might be far away and too busy to make you their top priority right now? Your mum and dad back home who don't speak a word of Spanish? Or your travel insurance company that has 24-hour service with skilled staff that speak different languages and who can quickly organize a search and rescue operation anywhere in the world?
Remember that travel insurance is not just about paying the bill - it's also about getting you out of there, be it by truck, boat, helicopter or lama and into a safe and good hospital.