If you are travelling in the EU then make sure you have a current EHIC – European Health Insurance Card. These are free, you can apply yourself and should not pay an agent to obtain it for you. Learn more and apply using the official site here.
If you already have one, then check it is current. According to the BBC over 5 million UK citizens have EHIC cards that are out of date.
The EHIC allows you access to free or reduced cost health care in most EU countries, but there may be restrictions and it is unlikely to cover repatriation costs or ancillary costs of certain sport accidents, eg the cost of getting down a mountain if you are injured skiing. So it is not a substitute for comprehensive health or travel insurance.
If you are travelling outside of the EU then you must consider having adequate health insurance as part of a wider travel insurance policy. Check it covers any sports or activities considered ‘dangerous’ or excluded if you intend doing these while overseas. Also check your age is covered and that if you have a multiple trip or annual policy that any restrictions on total or consecutive days cover wont impact your planned trip leaving you uninsured. This applies to any EU or worldwide policy.
Shop around, often the best value is an annual &/or family policy.