What should I do with old furnace filters?
While I cant think of any DIY project, you may wish to call or research as to whether that particular filter vendor provides recycling. If you have any friends or family with a fireplace or wood stove I bet they burn well. Barring both of those, all I can suggest is to buy washable filters in the future. You will pay a higher premium up front but it should pay off in the log run (and help you keep some junk out of the dump).

EDIT: Before burning, you should check that the filter is free of metal frames or added chemicals that could be harmful. If those are not present, the filter could also be shredded and composted (maybe).