Travel insurance is pretty much a must, whatever country you are going to visit, but its cost and necessity does vary country by country.
For some countries it is a legal requirement, for others things like medical costs, as per USA, make it pretty crucial for most people.
Some countries are safer than others, and some parts of some countries are safer than others.
Insurance companies require people to follow any travel advice that their national government gives out about the state of a country, and how safe it is to travel there.
Governments of other countries than your own will also have travel advice for their citizens, which will be useful to follow.
Whilst travel insurance will usually cover most medical conditions, albeit at a cost, if you have a condition such as epilepsy it is worth remembering that some countries still have quite a cultural and social problem with people who suffer from it.
It is also worth researching the medical system of any country you are going to, especially if you are visiting any remote areas of that country.
Also check if your insurance company will pay any medical bills directly to the hospital, or if you are expected to pay them and claim the money back from the insurance company.
Below is a list of articles about travel insurance to different countries, including some general travel tips and information on safety, airlines, sports, and health systems etc.