What to do with ground wire when installing ceiling fan on ungrounded branch circuit
The green wire is a ground wire.  The purpose of it is to cause the breaker to trip or the fuse to blow if a short circuit develops.  The majority of the time you can just hook up the white (neutral) and black or blue wires and never have any problem.  

HOWEVER! If a short circuit does develop you may burn the place down!  

If you have a metal box connected to metal clad flexible conduit or EMT you should be able to screw a #10 screw into the box and fasten a green wire to it completing a ground.  Whatever you have, there should have been a bare copper wire coming in to the box with the black and blue. Some do it yourselfers figure they aren't important and cut them off.