I am in US and would like to travel on Eurail.?

So I guess you are not the U.S. citizen, right? It depends on what countries you are willing to visit. If you really want to COMPLETE Europe, you might want to apply for several visas, but if you only visit places like France, Germany, Italy, and other major Eastern cities, you'll only have to apply for one Schengen Visa. Pick the country that you plan to arrive or stay for the longest period or the one that think it's easier to apply, search for the emby website on the internet, and do as they require. Check the list of countries in Schengen Area from the website below.