Taking Dogs on Trains in Japan

Japan Rail (JR) does allow passengers to travel with their dog on trains, as long as the dog is enclosed in a crate that fits their regulation sizes. JR does however reserve the right to refuse transport if the train is crowded etc. The charge for a crate is 270 JPY.

The total weight of the crate and dog, must be under 10 kilograms.
The crate must not be longer than 70cm.
The total size of the length + width + height must come to under 90cm.

Here's the link for JR's Japanese sight with the above regulations listed

When it comes to traveling with dogs, Japan is not a very pet friendly country. Almost all hotels do not accept dogs, and public transportation for anything other than a small dog, will be a no go.  Pretty much any establishment that serves food will also not allow dogs on the premises (outdoor cafes are often an exception). Keep this in mind if you are thinking of getting around in Japan with a dog!