Hitchhiking is a common way of travelling in some parts of Europe, especially in former eastern bloc countries. It can be a pleasant way to meet lots of people, and to travel without spending too many euros. Don't forget to check out the tips for hitchhiking.
Note that in the former eastern bloc, you may run into language problems while hitchhiking, especially if you speak only English. It is not advisable to hitchhike in former Yugoslavia, for example between Croatia and Serbia, because you could run into big problems with nationalists. Between Croatia and Slovenia it's usually not a problem. In Moldova and Ukraine, it's better to take train or bus. In western Europe, especially in the Netherlands and Germany, it's easy and fast to hitch-hike.