Depending on the amount of the accident settlement you are seeking, the attorney may be your safest avenue. The average citizen will have little chance in a high dollar case or one that is complicated if they elect to try to represent themselves.
On the other hand, if you are only asking for a small amount in a simple case where you were held blameless, you may opt to pass on a lawyer. The fees for the lawyer would be subtracted from any payment to you.
Every case is different, but an accident attorney is good to have for several reasons. If the attorney is experienced, he/she probably knows some of the people in the insurance circles, which might make negotiations easier. An attorney will be aware of all the national and state laws as they apply to your case so that all the bases will be covered legally.
Even more importantly, attorneys will understand the basic fee base and know how much you can and should ask for in your settlement. Because negotiations make up a large part of what attorneys do, they will usually get a higher settlement than you could hope to get on your own. Naturally they are motivated to do so as they generally work on a percentage based fee in these types of cases.