I would always recommend taking out travel insurance when making a travel booking. I think that it is money well spent for peace of mind. You just never know what might happen when you are travelling and you don't want to end up seriously out of pocket if your luggage is lost or you have an accident. I know that EU residents are eligible for health care in member states but this does not cover you for every situation, e.g., an air ambulance home. Evidently 15% of UK residents don't bother taking out travel insurance.
With most package holidays you can not book a holiday if you do not have travel insurance, so this will serve as a reminder. The insurance offered by travel agents is nearly always much more expensive than cover that you buy independently. However if you are booking an independent holiday you should remember to ensure that you have travel insurance.
Don't just look at the price of the insurance; also examine the levels of cover for various incidents, and the excess deducted from claims. Will the sports or activities you do on holiday be covered or be considered hazardous and excluded from the cover? If you take at least two one-week holidays in Europe per year, it is usually worth taking out a policy such as Endsleigh annual travel insurance which covers all your trips for a single premium.
It it also a good idea to leave a photocopy of your policy with a relative or friend in the UK. Remember to carry the 24 hour emergency contact phone number for the insurance company with you at all times.
I'd recommend that you get at least a couple of quotes to compare the price and level of cover.