Sometimes people get confused about the term "Travel Insurance". Some travelers and insurance companies describe Travel Insurance as medical insurance while you travel, while others simply describe it as insurance for cancelled flights and missing luggage. No matter what name you give it, you will want all of these things.
Technically speaking, and for the sake of clarity, Health Insurance is for medical needs, and Travel Insurance is for other travel problems such as canceled flights and lost luggage.
Health insurance in the U.S. has been a hot topic lately. Make sure you check your insurance plan to find out what it covers when you travel abroad. Many domestic plans do not cover medical needs while abroad, while others have extreme limitations. You will likely need to purchase extra insurance, especially if your trip will be long-term. You could purchase this international health insurance through your existing insurance company, but it will probably be much cheaper if you obtain insurance from another company that specifically sells international health insurance. In addition to providing health insurance, many of these companies also throw in extra coverage for canceled flights, missing luggage, and other mishaps.
If you are American, it is important for you to have continuing medical coverage within the U.S., even if you will not be at home. Having a gap in your U.S. health insurance means that you could be denied coverage later in life, especially if you have or develop a "pre-existing condition". Laws to prevent such problems have recently been passed, but do not take affect for several years.
If you live in a country that has government provided healthcare, make sure you investigate what your options are when traveling abroad. You may also need to purchase extra insurance, and your travel destination(s) may affect whether or not you are covered. If you are traveling to the United States, your home country's insurance is most likely worthless and you will need to purchase special insurance. Consider this cost when adding the U.S. to your list of destinations.
To get you started, here are a few commonly used international medical and travel insurance companies. We've never had to make an insurance claim while abroad ourselves, so we can't specifically recommend any particular company. Look into all of your options and make the decision that's best for you. The Lonely Planet forums often has posts about people's experience with filing insurance claims while abroad.