When it comes to bugs you learn very quickly that Japanese bugs are much bigger than the ones you have back home (speaking as an Englishman). When you come face to face with something that could take on Peter Parker, Godzilla and King King start to look possible too. Thankfully, the bugs I've encountered so far have been mostly harmless.
Dragonflies are large and clumsy. I'll often be smacked in the face by one when I'm walking around. They range dramatically in colour and markings, and are guaranteed to make you jump when they flop into your cheek or neck. In mythology Japan was called Akitsushima, which means 'Land of the dragonflies.' I can believe it - a day doesn't go by without me seeing at least a few dozen of them.
Moths here are also huge. At Achi Obon festival I saw one that must have been the size of my hand! I thought it was a bird at first, then had to double-take as it's ghostly white form glided away through the night. Moths also vary in size, shape and colour.
Butterflies I haven't seem many of, but the other day at school a dark shadow passed by the window. I turned to see a large jet-black butterfly landing in the flowers. It was bigger than my hand (and my hands are 95%ile male), and despite its innocent flutter gave off a rather sinister vibe.
Rhinoceros beetles I was introduced to by my shogakko students. One lunchtime they were playing with something in a little dirt-filled tank at the back of the classroom. I ambled over and asked them what they had. The student turned around with the largest frickin' beetle I've ever seen stuck to his finger. It had a long dark horn protruding from it's head, and didn't seem at all fussed about being manhandled by a clutch of students.
I've also seen ants, horseflies, mosquitoes, spiders... all of the large variety. I'm more than happy to keep these at some kind of distance though!