Wars often force big changes. Some produce bigger countries by conquest, others turn the borders into fortresses. Before World War I, people could travel all around Europe and into Russia without having a passport. There might be a mass of smaller countries nestling in the midst of larger Empires, but there was trust between the people. Even though Britain and Russia fought each other, this did not change. But, come 1918, there was a complete loss of trust, and both passports and visas became necessary to pass from one country to another. After the end of World War II, there was a general sense that nationalism was a bad thing, so people came together and formed the United Nations. Trust between countries improved and many allowed people to pass across borders without passports. In Europe, the key moment came in 1985 with the signature of the Schengen Agreement.
Now you can drive through twenty-six European countries without having to stop and produce any identity documents. Although this is only about half the land mass of the United States, it allows the 400 million population to move freely (there are just over 300 million Americans). This is a very big plus for American visitors. Once you have passed through the immigration controls at the airport, you can pick up your cheap car rental and drive it more or less wherever you want. Obviously, if you break any of the traffic laws, the police will want to see documents proving who you are and showing you have the right to drive this particular vehicle. Other than that, you can enjoy nonstop travel.
This freedom may come with a price tag. You have to pay an additional fee to pick up at one point and drop off at another. So unless you are going to drive a big circular route, you may have to pay a little extra on the rental. However, since most of the companies with branches in multiple countries offer cheap car rental, this is not a problem. You should, however, check whether there’s a cap on the milage. It’s best to avoid shocks when you hand the vehicle in and the service staff check the odometer reading.