When I first started practicing law, anyone who wanted to check a person's criminal background had to go down to the courthouse and physically look up some records. In those days, getting a record cleared had a real, demonstrable effect. Those days are gone and we live now in a post-privacy world where it is impossible to erase history. That said, there are procedures available pursuant to statutes that give you the right to "expunge" or "vacate" some of the information from public view. These statutes give you the right in some cases to state that you were never convicted. Don't expect law enforcement agencies to destroy their records, they are rarely ever required to do so and will always keep some information that is not available to the general public.
The problem with record clearances is that they are usually only directed at official record keeping agencies (like law enforcement or court staff) and don't adequately address the most common scenario, i.e., the private Internet-based background search firm. Here's a scenario that is happening more and more often: Employee fills out a job application and answers "No" (as he is legally entitled to do) to the question asking if he has ever been convicted of a crime. Employer hires a background search firm that confirms that "yes, he has no criminal record, but let me tell you what he did in 2004 ...". The employer is disappointed that his applicant lied on the application, the employee never gets the job and never learns why.
Record clearances can be helpful in certain contexts, but can also provide illusory benefits. For a full discussion of this procedure, talk to your attorney and ask what risks you are likely to face.