In the US, we've tried to circulate a dollar coin a few times, but it never seems to work out. There was the large, silver dollar followed by the smaller gold-colored ones. Most recently, I got a dollar coin with George Washington's mug on it (goodbye Sacagawea). According to this reliable source, there's a new president's face gonna come out on one of these here coins for a little while. I bet you can guess where I got that darned dollar coin...that's right!...the Post Office!! It seems like they're the only ones who use it. Try putting that coin in a non-stamp vending machine.
The smallest denomination paper bill in Euros is worth 5. There are coins for 1 cent, 2 cents, 5 cents, 10 cents, 20 cents, 50 cents, 1 euro, and 2 euros. Although it took a little bit of getting used to, I ended up liking the 1 and 2 euro coins. It was also initially weird not to have quarters. I just don't think that Americans are willing to carry around and use one dollar coins. Why do we keep making them? Perhaps they'll be worth something to collectors in 50 years.