Who is the president of Japan?

Japan does not have presidents. Japan is a constitutional monarchy. They have an emperor, who is the head of state, and a prime minister, who is the elected chief executive of the country.

The current Prime Minister is Shinzo Abe, whose term started on the 26th of December, 2012.
Akihito is the current emperor which is more like a president

-There is no President in Japan. There is an Emperor, who used to be treated as part God until WWII, and now after the war, the Emperor lost most of his power and is now just a figurehead.

Prime Minister is the closest to "president". As of now (Nov 2012), it is Yoshihiko Noda.

The Emperor is currently Emp. Akihito, and as of 2012, he is in his 24th year of reign.