In many states, this is called an order of non-disclosure. There are two procedures- expunction or non-disclosure. Expunction is available for arrests and charges if there was no conviction or if the conviction was overturned or you were pardoned. Non-Disclosure Orders make the matter "hidden" from most parties for lack of a better term, but can still be located by law enforcement and certain entities. A local attorney can help you through the procedure.
It depends upon what you are trying to seal and how long it has been since the matter was closed. there are several attorneys who specialize in this area and they are on this web site, i suggest you contact one, it may be worth it.
The first answer does not apply to Massachusetts. In Massachusetts, there are actually two procedures-- sealing and expungement-- but the latter, expungement, is almost never used, since it is mainly for cases of mistaken identity and/or where the judgment is the result of fraud upon the court. In fact, in Massachusetts expungement is so rare that in my experience, many court clerks have not heard of it.
So, how do you get your record sealed, and what does it mean? Although the procedure may vary slightly from courthouse to courthouse, in essence it is a two-step process. You must first bring a motion to seal records in each courthouse in which you have records of convictions you wish to seal. Hence if you were convicted once in Dorchester and once in Lowell, and wanted to seal both, you'd have to do two separate procedures.
At that first hearing, the judge will determine whether you are eligible to have your records sealed. If so, the DA's office is supposed to attempt to notify any victims of the crimes which resulted in the convictions, and the request to seal records is posted in the courthouse for public view for 30 days. After that period elapses, a second hearing is held, at which anyone (including any victims) may appear and voice objections to sealing the records. Then the judge will make a decision.
If your records are sealed, even you will not be able to request them in the future in the normal way. Hence it is advisable to get certified copies of important records from your case(s) before the second hearing, for example to prove that a case was dismissed, if it ever becomes necessary.
Recent legislation went into effect in Massachusetts, changing the prerequisites for sealing records, which is something to be aware of before you file. I also suggest Googling on "Massachusetts CORI Reader" for more general information about CORI.
There are 2 main methods for sealing: an action under G.L. ch. 276 s. 100A and an action under ch. 276, s. 100C.
100A petitions are filed when the charge you are seeking to seal has "aged out", that is, misdemeanors older than 10 years and felonies older than 15 years. A 100A petition is filed directly to the Commissioner of Probation, and must be allowed if all statutory requirements for sealing under 100A have been met. These requirements are, in addition to the 10 or 15 years having elapsed, are that you have had no intervening convictions in the 10 years preceding your request to seal and that the charge(s) you are seeking to seal are not charges that the statute specifically excludes from sealing. Note that on May 4, 2012, amendments to 100A go into effect and will shorten the waiting periods to 5 years for misdemeanors and and 10 years for felonies.
100C petitions do not require a waiting period, but can only be filed when the charges have been dismissed without a period of probation, or nolle prossed, or when there has been a finding of no probable cause, or if you were found not guilty. A 100C sealing petition is filed in the court where the charge originated, and the reviewing judge will have discretion to deny your petition if the judge does not feel that you have shown that "substantial justice" requires that your record be sealed. A 100C petition involves the 2 hearing process that the previous poster described. Note that when the amendments to 100C go into effect on May 4, 2012, the prohibition against dismissals that resulted after a period of probation (i.e. a CWOF that eventually led to dismissal) will be removed, meaning that charges that were CWOFs that were ultimately dismissed can now be sealed under 100C.
A third method of sealing applies only to first offense drug possession crimes. I have included a link to a Legal Guide I wrote that covers that topic.
My office handles sealing petitions on a regular basis, and I would be happy to discuss your case with you. There is a right way and many wrong ways to go about attempting to seal your record. Make sure you do it the right way the first time.