Very good answer from Nomad! But they are a bit more expensive. If you can't afford a metal roof you can put the rubber over the old asphalt. Just make sure that you scrape off all loose rock if your roof is tarred and rocked. If you have any existing leaks you need to pick up a bucket of roofing compound and apply it to ensure no chance of leakage. If this roof is on an add-on which is attached to your existing house then make sure you apply a seam of tar where the roof attaches to the main body of the house. Then lay your rubber. After that you will want to add a layer of rolled roofing over top of the rubber.
I have seen it done both with and without a substrate on this old house. I would suggest a standing seam metal roof they last for upwards of fifty years.here is a page on rubber roofs . Hope this answers your questions. Hubpages.com/hub/Providence-Rubber-Roofing