One could buy a JR rail pass that is good for a set number of days (7 is common) Works on all Japan Rail lines as well as most Shinkansen (bullet trains), but not the private lines in Tokyo/Osaka. Must be purchased as a tourist from the US. I don't recall any paperwork being required. Used to be purchased on line, ticket was good for a set number of days, and it was "activated" upon first usage in Japan. It was cheaper than buying a ticket physically in Japan, unless it was a one time, one way trip on the bullet train.

http://www.japanrailpass.net/eng/en001.html for details and current restrictions

My info could be a little dated, I moved back stateside from Japan in 2005.