If you are going on holiday, either for a couple of weeks in the sun on a remote island or a few days driving around Europe, then it is always recommended to take out travel insurance. Granted you are unlikely to have to claim on it, but there are a whole host of reasons why you might need to claim on it including illness which could range from tropical diseases to flare ups of existing illnesses.
While you have the insurance as a safety net, there are also things that you can be doing to lessen the likelihood of any illnesses, thus avoiding any disruption to your holiday.
A good First Aid kit is always a good idea, especially if there are illnesses or complaints that you are predisposed to. Even if you have medical insurance, you will not want to be leaving the sandy beach to find a doctor for a repeat prescription for a bad back or an unexpected asthma attack.
Make sure that you also check the need for any vaccinations before you go, your local surgery will be able to advise you and thinking ahead might just prevent some nasty disease.
Check into the medical arrangements in the country you are visiting as some countries have reciprocal agreements for healthcare and you need to know the situation before you go in case of any illness.