It could also be algae. you should take a either a sample or a picture to your local garden center. They carry products that will take care of whatever issue you have.
You can usually apply these with a hose end sprayer so you don't have to climb on the roof. If this isn't an issue with your house, you can stand on the roof and spray the shinges that way.
Home Depot used to carry a product that was used for algae, but I would check to see if they still do.
Ron

Ron - Thanks for your thoughts. I did some searching on Google and decided it probably was algae. The suggestion I found online was to use an "oxygen bleach", so I mixed up some of the oxy-clean I had in my laundry room. It took a couple of applications, and scrubbing with a moderately stiff brush, but it looks good now. There was also a suggestion to install a copper strip to help keep new moss or algae from growing, but I haven't decided if I will do this... or just wait and see how long the cleaning lasts.