I've travelled in the USA by train on many occasions. It's probably the most relaxing, comfortable and civilised way to see the country (and meet the natives), although not the fastest way to get around. Prices are very reasonable, especially if you buy an Amtrak pass. Useful information can be found on the USA by Rail website: www.usa-by-rail.com
Yay! Amtrak! I love taking the train. You have more room on Amtrak than probably any other form of transportation, and you can see the country you're traveling through. Watch out for some of the downtown stations in some cities. The ones in St. Louis and Kansas City are not so nice, but there are other stations in both metro areas that are better. Not that they're scary, just maybe not as nice.