If you charge VAT you will know that for non VAT customers across Europe you must charge them VAT like anybody else in the UK. (Read more here)

This means there are a lot of countries to setup with the current 20% VAT rate.

In WooCommerce you have the option to upload your Tax rates for all regions.  Here is a CSV file of all European countries, pre-configured to charge 20% Tax.

If you are looking for a way to validate EU VAT registered businesses, there are a number of plugins available, including one form WooThemes EU VAT, that will check and validate EU VAT numbers and help your website decide if you need to charge VAT on the order.