I live in the original Metro town, Stockholm! A lot of people leave the paper on the seat or folded over the odd handlebars by the windows on the trains. And most trains and buses are cleaned of papers at every end station, because it builds up so fast. On buses and "surface" trains I think it's okay to leave the paper for the next traveller, but it shouldn't be done in the subway because of the fire hazard.
We currently have two free papers here, Metro and City. Only Metro is allowed to have paper stands by the public transport system, so City has people handing them out instead. This means a lot of people grab a fresh City instead of picking up a used one on the train.
Good thing Sweden has a lot of trees and paper mills.