Tom Loosemore has an interesting discussion of when you are liable to pay the license fee. Apparently in the UK, you have to watch the BBC in order to have to pay license.
In Denmark it is enough to be in possession of a mobile phone (or any other electronic device) that has the capability to show one of the national TV channels:
It looks like there is still some way to go here in terms of harmonisation within the EU, but watch out if you borrow a computer from a friend in Denmark, you may have pay a license fee while you browse the your Facebook profile and enjoy a latte in your local café.