Is it true that in the countries in Europe you can use any mobile phone with any carrier?

Someone was telling me that when cell phones hit the scene the European governments purposely enacted laws that cell phone manufacturers and cell phone providers could not make exclusive deals. Here in America for instance if you want an iphone, you must sign up with AT&T, no choice. So if you love a phone, but hate the service you get with AT&T, or the prices they charge, you are in a quandary here. I hate it. I think it prohibits wide open competition.