In my book, I discuss how the "Schengen shuffle" will allow Americans and others who qualify for a standard tourist visa to stay in Europe for a year or more, by leaving the Schengen area at the appropriate time and taking advantage of countries that allow a longer stay.
Now, Matt Kepnes of Nomadic Matt has a recent update that clearly shows the countries covered by the Schengen 90-day visa, as well as outlining which countries offer their own visas for longer stays. (You cannot work, and you must have health insurance coverage--more on that in a later post.)
What's more, there are countries (for example, Denmark) with little-known reciprocal agreements with the U.S. that will enable you to stay for an additional period if you enter from another Schengen country and leave without exiting through another Schengen country. Check out Matt's blog post here.