By filing a formal motion with the court, you can seek to have a conviction taken off your record in a process known as expungement. The procedure depends on whether the conviction was for a misdemeanor or a felony, the punishment imposed and your age at the time of the conviction. By expunging your conviction, you are essentially undoing the conviction, restoring you to your status before the crime. The greatest benefit to having a case expunged from your record is the ability to tell private employers that you have never been convicted of a crime, truly giving you a second start in life after a conviction. There are certain limitations to what can be expunged and the rights you have, so your case should be discussed with an attorney. After discussing your options, your attorney can file the proper motions and paperwork to get you started toward clearing up your record.
**** Update ****
In January 2011, the law will change to allow non-vehicle infractions to be expunged as well!