Hyperdia covers all railway lines and domestic flights schedule. This is the best website and help you to build your itinerary. It is simple but a bit tricky to use. Please see the other post, Hyperdia perfect guide, train timetable and route search engine. I show you everything about Hyperdia in this post.
JR Group’s website
All JR companies except JR West have English website and show some timetables.
JR Hokkaido is doing good job. They have all limited express trains, such as Super Kamui, Super Ozora, Super Hokuto and more, overnight express Hamanasu and most of local trains! Some of local trains are not on the timetable. But I think this is enough for the tourists from other countries.
This website show you the timetables of Tohoku Shinkansen, Joetsu Shinkansen, Nagano Shinakansen, Akita Shinkansen, Yamagata Shinaksen, Narita Express, Odoriko/Super View Odoriko, Nikko/Kinugawa, Super Azusa/Azusa/Kaiji, Hakutaka and Super Hitachi/Hitachi. These are only trains that can be reserved online in ALL JR TRAINS.
This does not show any overnight trains, such as Cassiopeia, Hokutosei, Sunrise Izumo, Sunrise Seto and Akebono. And these overnight trains cannot be reserved online either.
This website shows the timetable of Tokaido Shinkansen between Tokyo and Shin-Osaka.
Westbound (from Tokyo to Shin-Osaka) | Eastbound (from Shin-Osaka to Tokyo)
This website does not show other JR Central trains, such as Wide View Hida, Shinano, Wide View Nanki.
You are able to find the timetables in the middle of the link above.
It shows you the timetables for Sanyo Shinkansen (Shin Osaka-Hakata), Haruka (Kansai airport-Shin Osaka/Kyoto), Thunderbird (Osaka-Kanazawa/Toyama), Kuroshio (Kyoto/Shin Osaka-Shingu) and Kinosaki/Konotori/Hashidate/Hamakaze (Osaka/Kyoto-Kinosaki Onsen).
JR Shikoku has English website. But it shows the timetables in Japanese. They put the numbers on all JR Shikoku stations and mention how to read Japanese timetable. However it is too complicated to read. I recommend to use Hyperdia.