Japan is covered by an extensive and reliable network of railways. 70% of this is owned and operated by the Japan Railway Group, more commonly known as JR Group (JRグループ). This consists of six passenger railway companies of JR Hokkaido, JR East, JR Central, JR West, JR Shikoku, and JR Kyushu, and one nationwide freight railway company. Together they operate a nationwide network of regional and local train lines including Shinkansen (新幹線).
The remaining 30% belongs to other private railway companies mainly in urban and suburban routes such as Tokyo and Osaka areas. Note that you cannot use JR Pass on these lines.
Here you can find information on all 6 JR groups.
JR Hokkaido JR北海道
This shows timetables for all limited express trains and many local trains.
JR East JR東日本
This shows the timetables for Tohoku Shinkansen, Joetsu Shinkansen, Nagano Shinkansen, Akita Shinkansen, Yamagata Shinkansen, and limited express trains such as Narita Express.
JR Central JR東海
This shows the timetable for Tokaido Shinkansen between Tokyo and Shin-osaka only.
JR West JR西日本
JR West route finder is a useful tool to find out train timetables including Shinkansen and connecting local trains.
You can simply input departure station and destination station with date and time of travel, then the finder suggests several options for you to choose from. It even lets you choose types of trains, so you can search Shinkansen options except Nozomi/Mizuho, which is useful when you use Japan Rail pass.
The site also provides timetables for Kansai International Airport access from various stations together with useful route maps and major station maps.
JR Shikoku JR四国
Although the website for JR Shikoku is in English, the timetables are in Japanese. You could decipher the timetable using the station number, but it is complicated. You may prefer to use Hyperdia mentioned below instead.
JR Kyushu JR九州
This provides timetables for Kyushu Shinkansen and all limited express trains in Kyushu.
'Hyperdia' is a service which offers timetables and related information for railways and flights in Japan. You can search for the optimal route and the fare information from starting point to your destination.
If you plan to use trains in Japan, you may want to consider buying a Japan Rail Pass (or JR Pass) before you arrive. You can find further information on the link above.
If you buy individual train tickets you have the option of getting tickets printed with English information.