The idea of the paper is to investigate how much the online user privacy is respected by website owners, and how online privacy can be improved. We first focus ourselves on issues like possibilities of misusing personal data, data collecting and user-tracking. Then we give a short report about legislation in the EU concerning user privacy. Some facts about user confidence are given as well. They are follows by a brief list of hints for the users to protect their personal data when surfing the Web. Then we give an overview of actions website owners should take in order to support user privacy. Finally, we present the results of our investigation of the condition of user privacy in practice, and give some suggestions on its improvement.