I have traveled abroad a number of times, but this past trip to South America was the first time that I purchased an insurance policy. While there are a lot of great options out there, I went with the company that Lonely Planet suggested - World Nomads. More information about the company can be found at http://www.worldnomads.com/
The decision to invest in insurance was made primarily because I was concerned about having a health issue abroad. Little did I know that what I would be using it for would be to cover the cost of a new phone after my iPhone 5 was stolen in Cusco.
After my phone was stolen, I worried that the insurance would only cover the initial price of the phone ($200) and wouldn't cover the cost of a new phone without contract (more than $400). I also worried that I never saved my receipt and wouldn't be able to provide proof of purchase. Neither of these concerns turned out to be actual problems.
World nomads allows you 90 days after the termination date of your policy to write a claim, so once I got back to the States, I immediately went to the Apple store and asked if they could reprint my receipt. Within minutes, that issue was resolved. Plus, I was able to purchase a new iPhone while I waited. Next, I photographed my police report from Cusco, and both the old receipt and the new one right from my phone and uploaded them to my claims page on World Nomad. It was a very simple and straightforward process. I waited a couple of days and found out that they would be sending a check for the cost of the new phone ($400) to my house, and that I should receive it within 30 days. I waited 5, and the check was already in the mail!
I couldn't be more grateful that I purchased an insurance plan. I would recommend one for any long-term trip abroad. I don't think it's necessary for traveling in the US or while traveling for short trips, but it definitely came in handy for me! I do recommend keeping photos of your receipts for big ticket items in dropbox or in the cloud. They would have been handy to have had while I was traveling. I also want to caution that their policy does not cover any cash that is stolen. That's just something you'll have to be extra careful about.
You never know!