You probably have absolutely nothing to worry about, but the sake of science, I will answer to the best of my ability.
Japan has bears (if you encounter one, I'd be amazed, though), monkeys (which are usually fine, but don't get too close!), wild boar (again, usually nice, but they can kill), giant bees called suzume bachiツ (usually not a threat), giant centipedes (and I mean HUGE!), and that's what I can think of off the top of my head.
There are probably, as Hachiro pointed out, poisonous snakes and spiders, too. I know the spiders can get to be the size of your hand out in the countryside, as I have seen them!