Europeans travelling in Europe need to worry about this form in addition to a regular travel insurance.
Any national of an EEA country (and also stateless people and refugees within the area) can obtain form E111, which proves that you are entitled to free or reduced cost emergency medical treatment in any other EEA country .(EEA = European Economic Area, ie the European Union plus Iceland, Liechtenstein and Norway). Depending, that is, what kind of benefits exist in the country you are visiting. The form entitles you to the same kind of health benefits as a national of the country. To cover treatment in a private hospital, for instance, you will normally need your travel insurance.
Other terms, it seems, vary slightly between countries. The form covers its holder and holder's spouse and also their children. In Norway, children up to the age of 25(!) are covered by the form. In the UK, it covers children to the age of 16 - or 19 should they still be in full time education.
In Norway, I was told that I need to get mine stamped/renewed once a year to keep the same form for three years. In the UK, it stays valid indefinitely, provided you don't move out of the country. Also, in the UK it appears you can get the form approved by any post office, whilst I needed to pick mine up with the local office of the National Insurance Service (that's Trygdeetaten to you Norwegians).
Oh, and don't worry if your form is in your own language only, it looks the same in all languages of the EEA, and each field is numbered in the same way on all forms.
I wanted to node this, and found it was a nodeshell. How convenient.