I jumped on Nancy's suggestion of newspaper as a collection device because it enables easier composting and doesn't waste plastic bags. It is possible to dump a dog turd from a poop bag into a compost bin, but the newspaper allows it to drop out easily and, if you are careful, the poop pickup bag can be used repeatedly.
In an effort to further reduce plastic bag use, I plan to transition to using paper bags to hold the newsprint protected poop. It's just a matter of being particular where I shop and making sure they offer paper bags. I might have to start buying wine by the bottle :).