The answer to that is YES! Even though some people believe that the disposable plastic bags break down and eventually become nothingness...they have no proof. They do know that some things effect how fast a bag breaks down and is no longer visible to the naked eye..but, the plastic particles are still there (we just can't see them like when it was an entire bag).
You can read a great article about The Truth About Plastic Bags Decomposing over at The Daily Green.
Even IF the plastic bags were to completely break down into a natural state after a certain amount of time, should cities and states still ban them from being used?
It's not just the biodegradable facts that come into play when talking about how harmful plastic bags are. It is the safety of animals that may be noticed the most. Recently I posted a video that shows what happens to a sea gull that finds a plastic bag ( Plastic Bags Kill Birds). I know that many people may not care much for seagulls but, they are part of the environment . If a gull will eat the bags I think we would be stupid not to think other birds wouldn't. We also know that sea turtles eat floating bags because they think they are jellyfish.
My suggestion is to help the environment by getting yourself reusable fabric bags to take with you to the store on every visit. It really isn't that hard to do. How often do you leave the house without your purse or wallet? Seldom I bet so, just get into the habit of remembering to take your fabric bags out to the car after you've unpacked your groceries. Heck, set or hang the bags by the door so they are easy to see on your way out. Every bag that you save is helping the animals and earth around you.