Nineteen countries now use the Euro as their currency. Fifty states use the Dollar as their currency. While that comparison is correct, it is a bit misleading for various reasons.
U.S. states are more homogeneous than Eurozone countries. Our states share a national government, including fiscal policy. We speak a common language, sort of. We've been economically integrated much longer, including free interstate trade since Constitutional times. We've had freedom of movement much longer, and so on.
Because of the scope of 50 states most of our trade is internal rather than external; so a change in the price of the dollar relative to foreign currencies has less impact on our trade than would the price of a Texas Dollar or a Colorado Dollar.
Theoretically, the Eurozone has been working toward more homogeneity so that its 19 countries are more nearly similar to our 50 states. But that experiment is only about 15 years old and it is far from complete. One implication is that the common Euro exchange rate with outside countries is likely to be more appropriate for some countries than others, as is a common monetary policy by a common central bank. Yet, a strong Germany, relatively speaking, shares these things with weaker countries like Greece, Spain, and Italy (Where do I put France?). I could almost generalize and say that the beer drinking countries of northern Europe will likely have different circumstances and needs than the wine drinking countries of southern Europe.
The recent rapid depreciation of the Euro should be very helpful to the countries with weaker economies, but that "help" will also go to the stronger countries. The importers and exporters of each country will be impacted, for better or worse, by developments in other countries. German car companies to the extent that they produce domestically for foreign markets will get a windfall caused, for example, by weak tourism in Greece and Italy. (I once spent 16 days in Greece and all I recall seeing were tourists.)
There is a phenomenon called the Dutch disease that originated by a development in The Netherlands that attracted foreign capital, which drove up their exchange rate, which harmed unrelated exporters and their employees. A version of the Dutch disease takes place with almost all developments that affects an exchange rate shared by others.
If France still had its Franc and Germany still had its Mark, and so on, local developments might affect their exchange rates and small changes would have large impacts. More of each country's trade would be foreign trade and be susceptible to correction through minor exchange rate adjustments. With a single currency, French-German trade becomes internal rather than external. Add in Italy and Spain and what is "foreign" trade shrinks further. With 19 countries sharing the Euro, it is bound to take larger movements in the currency to make a difference to a single country since the adjustment mechanism no longer works within the 19. In other words, the sharp decline in the Euro from the high $1.30s to almost parity with the dollar is probably more than would have been necessary for correction of a single-country currency.
This move from one to nineteen affects U.S. citizens as well, as we are getting a bad case of the Dutch disease. U.S. exporters and their employees, including multinational corporations that produce, sell and earn in many countries, are harmed by causes unrelated to them in one or more of the nineteen. We are forced into the European adjustment process and the impact on us will be larger than if Europe still had its individual currencies.
Of course, it works in both directions as the recent sharp decline in world oil prices resulted primarily from developments in Texas and North Dakota. If those two states had had their own currencies, the impact abroad, including both other states and countries, would have been milder - for good or bad.