Not technically Japanese food (it originates from Korea), but yaki-niku ("grilled meat") is so popular in Japan it would be rude not to mention it. You'll find each table has a miniature barbeque, upon which you place a variety of meats and vegetables to grill (or incinerate, depending on how many beers you've had). The choice of meats is huge (from beef tongue, every conceivable part of a chicken, to... well, you'll find out), and it's damn good fun too.
You'll find yaki-niku restaurants all over Tokyo. Gyukaku (www.gyukaku.ne.jp) has various locations throughout the city, with English menus available.
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