If you're not yourself a citizen of the European Union you might for forgiven for thinking exactly what benefits that instition has to offer you, the outsider. Surely it's just a big excuse for Europeans to get together and do what they do best - drink wine and invent new forms of bureaucracy?
Well, there is actually a little more to it than that. One of the advantages of traveling in the EU is that there are few internal borders: the day when each major road heading between France and Germany had a customs point and a frontier guard are long, long gone. These days there's no reason why you can't drive from Portugal to Poland, only having to stop to pay tolls on highways. In essence, it's just like traveling in the United States, and in some ways it's convenient to think of Europe as being a little bit like the US, although the countries of Europe are yet quite so closely federated as the states of the Union. For example, each still runs its own defense and foreign policy - not something that would be practical in the US, especially if you wanted to avoid a war between California and Texas.
If you're a US citizen visiting Europe, all you should have to do is show your passport when you arrive - along with your visa if you're over there for a long visit - and then you casn roam around within the EU at will. You must, however, remember to keep your passport with you at all times, as you are expected to carry a form of identification. You may also have to hand over your passport at hotels so that your presence can be registered with the local police. Some countries - Italy, for example - still technically require you to register at a local police station in person, although in practice nobody does this.
The exception to all the above, as you might expect, are the bloody-minded Brits. You will have to show your passport on entering and leaving the UK, as the Brits have exempted themselves from some of the internal border requirements. There's also no legal requirement to carry ID in the UK, though the government are currently trying to change this in the face of much opposition from the great mass of the people, who think it beneath their dignity to be treated in the way the French or Germans treat their people. If you're an American entering the UK you're very unlikely to have any problems: despite what you might hear, pro-American feeling in Britain is very strong.
The same cannot be said of all other European countries, especially France. There have been some stories recently about Americans visiting France running into unexpected customs hitches and minor bureaucratic tangles - nothing major, but irritating all the same. Whether these have all been unfortunate accidents, or if it's in fact a case of the diplomatically-marginalized French getting their own back, it's hard to say.