Be careful with this.

Not all countries give free cover, some will only reduce the cost.
Also, care must be given in a state run facility, if you use a private doctor or hospital it is unlikely that the EHIC will be accepted, leaving you to pay the bills yourself.
Most medical centres in and around tourist areas (especially in places like Spain) are private, placed there for the sole purpose of tapping into the 'tourist insurance' medical market.
Medical care is much more of an industry in many places on the continent, a concept that is very alien to us NHS groomed brits!

Plus, some countries make their health care free at point of use, which means you won't be charged. Others are not, meaning you have to pay the costs locally yourself, then claim them back. This is done either in country, or on return to the UK.
The EHIC also doesn't cover any costs for repatriation, so if you needed to be returned to the UK to continue any lengthy treatment the costs for this would have to be paid yourself.
An Air Ambulance from parts of Europe can cost as much as £30,000.
As the Department of Health say themselves, the EHIC should not be considered a replacement for private medical insurance, such as that provided by a Travel Insurance policy.