There's an excellent article in the Guardian online about how a small town in Devon, England has banned plastic bags. Read more here. The town has its own Plastic Bag free website.
This initiative was inspired by the documentary Message in the Waves, which reveals the terrible problem of marine borne plastic waste in the Hawaiian islands.
I carry a fabric carrier bag in my handbag at all times and refuse plastic bags whenever I can. A fabric carrier lasts for years and means that you can avoid picking up plastic bags from all the shops you visit. I also try to avoid buying products with lots of plastic packaging.
Of course there are problems with paper waste too, but paper is biodegradable and certainly doesn't cause the types of problems for wildlife at sea as shown in Message in the Waves.