JR (Japan Railways
) is the largest railroad company in Japan. The Japanese government
privatized its state-run company because it was incurring large amounts of debt. Since then JR (at least some branches) has been much more profitable.
JR runs commuter and freight trains in all four of the main islands. It is actually split into at least 9 companies: JR Hokkaido, JR East, JR West, JR Central, JR Kyushu, JR Shikoku, JR Freight, and two research divisions.
If you're a gaijin (or Japanese national living in a foreign country) planning to visit Japan, a good idea is to get a JR Rail Pass. They allow you to ride as many trains as you want (even Shinkansen), all over the country, for a period of 1, 2, or 3 weeks.