To the far west of Massachusetts is Berkshire County, which was founded in 1761 as one of the last counties to be formed in the state. You will have fairly good success looking up Berkshire County public records back to at least that date if not older.
The central state Registry of Vital Records and Statistics only holds records between present day and 1921. They are located in Dorchester and they will either accept mailed in applications for a copy of any Berkshire County public record, or you can visit in person. The service counter is open Monday through Friday. If you are in the Berkshire area, you can also stop at the local clerk's office in Pittsfield for the same service.
Records for the years 1841 until 1921 are no longer kept at the government offices, but can be found at the State Archives in Boston. You can do an online search of their holding from their website, though these are usually just indexes rather than complete records. You'll need to go to their research rooms to find the actual documents, or pay a fee to have staff do the look-ups for you.
For any Berkshire County public records that are older than 1841, there are plenty of them but not a simple way to access them. You will get the best results at the town clerk's office where the event happened. The county clerk in Pittsfield can probably help you find the right location.
Berkshire County Birth Records
You will be able to order certified copies of any Berkshire County birth record because there are no privacy restrictions in Massachusetts. The cost if you mail in your request is $28 but its only $18 if you visit an office in person. You need to provide the full name of the person, their date of birth and location where they were born.
Berkshire County Death Records
Berkshire County death records also have no restrictions, so orders can be placed for any records you need. Fees for these records are $28 by mail, and $18 for in person service at one of the records offices. For death records, you need to know the person's name, when and where they died as well as their parent's names or spouse's name.
Berkshire County Marriage Records
Marriage records are treated the same as birth and death records, and can be ordered from the same locations as listed above. To order a copy of a Berkshire County marriage record, you will have to provide the names of both parties, as well as the date and location of the marriage.
Berkshire County Criminal Records
Criminal records are not handled the same way as other vital records, and all Berkshire County criminal records are available through the state Department of Criminal Justice Information Services. You are permitted to order copies of your own criminal background files, and some other records are made public depending on the person's crime and sentence status. The cost to order these records is $30 each.