So far, I've always been lucky in terms of health and safety on my travels. I usually book my trip individually and don't take out travel insurance for the flight or accommodation, especially if I don't plan too much in advance and the trip doesn't cost a huge amount of money. I have my VISA credit card, which includes basic travel insurance if I pay for the trip by card.
Of course I wasn't that relaxed for my trip around the world. I knew something could potentially happen within 11 months. I booked all of my big flights with my travel agent (STA Travel) and also took out travel insurance. So it all depends on how willing you are to take risks, how big your budget is, how far in advance you book your trip and whether you have another option, such as insurance via a credit card.