This is one area where going green and saving money diverge. The cheapest renewable tariffs tend to cost more than the cheapest standard tariffs, so it really is a question of your personal politics. However, if you can afford to go renewable, then it's a help to the environment, and all the main comparison services allow you to compare renewable tariffs.
Twenty-nine states have deregulated electricity, natural gas or both. That allows you to shop for the supply portion of your bill from alternative providers who may offer rates lower than the default supplier – usually a utility. Delivery services and billing will remain the responsibility of the local utility as they own the power lines and wires that keep the lights on.