Don't get too excited by the thread title. But you can ride the Tokyo Metro subway for free (legally) if you are on your way to purchase a commuter pass. I thought some people might be using passes, but not aware of this service.
Commuter pass sales offices are only at a few stations. If you're not lucky enough for one to be available at the start or end of your route, obviously you need to find your way to a station that has a sales office. But Tokyo Metro will pay your round trip fare to that office from any other station.
Here's how to do it. First, pay cash for a regular 1-way ticket to the sales office. But do not use the automatic turnstiles. Instead, show your ticket to the station employee and tell him you are going to buy a commuter pass. He will stamp your ticket with a special stamp and wave you in. When you arrive at the station with the pass office (which is outside of the turnstiles), again show your ticket to the station employee and he will let you out.
Now, in the pass office, hand your ticket to the person at the counter. They will take the ticket away, and give you cash back for the full cost. When you complete the pass purchase, ask for a return ticket. They will ask you which station you're returning to, and then they will print a regular 1-way ticket for you to use. This ticket can be used normally, on the automatic turnstiles.
Official version of these instructions here. Enjoy!