Having a cell phone is quite handy in Japan. Cell phones can be purchased in cell phone shops around town. Required documents vary by shop so please check with each company. The followings are the list of major cell phone companies in Japan:

NTT DOCOMO

http://www.nttdocomo.co.jp/english/

au

http://www.au.kddi.com/english/index.html

SoftBank

http://mb.softbank.jp/en/