At least half of the theaters I've been to in Japan have special cheap showings, like matinees in the states.
The kicker?
It's the late show!
Yep, that's right. Unlike America, were the cheap shows are in the afternoon, it's usually the last showing of the night that's cheap in Japan. This applies less in the big cities, but you should still be able to find it. By cheap, I mean a ticket will run you 1200 yen instead of 1800. (About 6 bucks less.)