1: JR Pass. Good for the Shinkansen, local JR trains, and a few other things. Just wave it at the attendant to enter the station. $400 for two weeks.
2: Suica. Rechargeable card for the other trains and subways. Use it to buy things from vending machines, too. $10 minimum, but you'll blow through that.
3: Portable Wi-Fi. Order ahead or rent one at the airport and turn yourself into a roving hotspot. Never be without a connection. $95 for two weeks.
4: Google Maps. Always know where you're going and what train to get on. Japan is not based on a grid system. Requires the wi-fi. Free.
5: Spare Battery. Don't run out of juice. $Variable.
6: Beer. Technically not indispensable, but highly recommended. $5/bottle.