From what I experienced, European merchants do charge VAT as a part of the price: being from outside EU I can see prices listed on ebay.de and ebay.co.uk with and without VAT. Different EU nations have different provisions for taxation of privately sold / used items, so VAT may or may not apply in those cases.
Foreign merchants listed on European eBay sites do not charge VAT, nor they should: import duty is the job of customs office.