It actually is kind of cool. You can travel and even reside (including work permit, social security and even the right to vote locally - actually you have to be treated similar to the native citzens) where ever you like in more than 30 countries. You don't have to excange your money while traveling within 22 countries. Where ever you come in many areas the same or at least very similar rules apply in all these countries. Your even able to go to court against your own country and you might even rule out your countries supreme court (in case your human rights are endangered). You as well get financial aid for many things (i.e. building infrastructure, protecting cultural and ecological heritage, ...) but you will as well have to pay for that aid for others as well (with your tax).
With all that one should not forget that, other than i.e. the member states of the US, we are talking about more than 30 different, fully souvereign nations with their very own (at least) centuries old culture, heritage, languange and history. Despite all negative site effects this might have (i.e. common regulation leads sometimes to some, from your local perspective, very weird rules), it is a overall net plus for all its member states and a great, historical vision. As you might have assumed already, I like beeing a European citizen. :)