Shogi

Shogi is Japanese chess, which is a variant of an older form of western chess. The main differences can be summed up as follows:

Due to the drop rule the game is fantastically tactical and there are no endgames as in chess. The games always end with mating attacks on the opposing king.

A list of learning material:

Videos

YouTube has plenty of videos available.

General

Tutorials

Tsume

These are checkmate or 'endgame' problems in Shogi. Essentially the side to move gives check with every move and has a forced checkmate. I think for someone already familiar and competent in chess this would be a logical place to start after learning some move basics.

Bonus links for Go

Just to have it here: Sensei's Library is the most useful site for Go. There is also a famous anime series "Hikaru no Go" which contains some lessons at the end of each episode.

Some other links: