Massachusetts courts that kept records of genealogical value include:

1620-1865	General Court. This was an appellate court that gave rulings on estates. Its records are at the Massachusetts State Archives. Some records of this court are in the Massachusetts Archives Collections described in the “Genealogy” section of this outline.
1636-1693	County courts or quarter courts. These courts were originally called inferior quarter courts. Most of the records of these courts are in county courthouses, and many are on microfilm at the Family History Library. These courts were replaced in 1692 by the superior courts of judicature, courts of common pleas, and courts of sessions. Superior courts replaced the courts of common pleas in 1859.
1692-pres.	Superior courts of judicature. These courts were replaced by supreme judicial courts in 1782. These were courts of appeals. The records are at the Supreme Judicial Court Building, 1300 New Court House, Boston, MA 02108.
1822-pres.	District, police, and municipal courts. The first district court was established in Boston in 1822. The records are in the various local courthouses.