How long have martial arts been practiced in Japan?

It would greatly depend upon the definition of martial art and the sub-categories within them.

The Japanese SWord can be broken down into many different styles. So can Japanese karate.

In general, here is a partial listing:

* Iaido * Judo * Aikido * JuJitsu * Aikijitsu * Japanese Karate * Sumo * Ninjitsu * Kendo