In the book "The world without us" (web site links to a great "Daily Show" interview), Alan Weisman mentions that plastic has an incredible staying power; it takes over 1000 years to decompose. This might change in the future. For example, it also took bacteria a while to learn how to decompose wood.
Also, there is an island of plastic trash floating on the seas that is at least the size of Texas. So the following should be good news: "Teenager's Science Fair Project May Deliver Us From Plastic".