If you are looking for the timetable of Shinkansen or major limited express trains, try to find it on JR Groups websites. Otherwise you can check the timetables on Hyperdia.
JR Group’s website
JR looks Japan’s National Railway but it was privatized long time ago. And technically there are five different companies, JR Hokkaido (Hokkaido area), JR East (Tohoku, Kanto, Tokyo and surrounding area, Nagano), JR Central (Shinkansen Tokyo-Osaka, Nagoya and surrounding area, Chubu region), JR West (Kansai and Chugoku regions), JR Shikoku (Shikoku area) and JR Kyushu (Kyushu area). These JR companies offers timetable and fare search in each websites.
JR Hokkaido offers very simple and easy timetable. You can pick a route and find all express trains and major rapid trains timetable.
JR East timetable
This website shows you the timetables of most of limited express trains, Shinkansen and popular seasonal trains in JR East areas. It also shows you the timetable of JR Hokkaido trains.
JR Central timetable
JR West timetable
This website offers you the fare and timetable of not only JR West trains but also many of JR trains.
JR Kyushu timetable
You can find the updated PDF format timetable of most of express trains in Kyushu.
If you cannot find the timetable in the links above, please use Hyperdia to find it. Hyperdia covers all train’s schedules, most of domestic flights schedules, airport shuttle bus schedules and fare tables. This is the best website for a traveler who takes a train, and helps you to build your itinerary. It is simple but a bit tricky to use. Please refer the guide of Hyperdia in the link below: