You can apply on a country by country basis for trade marks in Europe, the same as you can in North America. You can also apply for what is commonly referred to as a Community Trade Mark (CTM) or you can obtain an International Registration pursuant to the Madrid Protocol. For a comparison of the two click here. Generally, my preference is to apply for a CTM. Materially, use in each separate country must be proved for a Madrid registration. The mark is examined separately in each country. Each country may refuse registration based upon significantly wider criteria than apply for a CTM trademark. So while on first glance a Madrid application looks simple, it is more expensive and will take significantly more effort to process to conclusion.