The Act of 1543 established the courts of Great Sessions in Wales, equivalent to the English Assizes, which continued until 1830 when they were abolished. Records for the Great Sessions are held at the National Library of Wales.

Powys Archives hold records pertaining to Radnorshire Quarter Sessions which were established by the same Act although records do not begin until the late seventeenth century. See also their Petty Sessions listing

The Crime and Punishment database  on the NLW site comprises data about crimes, criminals and punishments included in the gaol files of the Court of Great Sessions in Wales from 1730 until its abolition in 1830. The Court could try all types of crimes, from petty thefts to high treason. In practice, most of the petty crimes were heard at the Courts of Quarter Sessions, whose records are held by the Welsh county record offices. Details about these records can be searched at Archives Wales. The records of the Court of Great Sessions do not include cases tried in Monmouthshire since that county formed part of the Oxford Assize circuit, whose records are held by the National Archives. There are, however, a number of cases of Monmouthshire interest on this database.

There is a Wales related Crime and Punishment section on Wales - Genealogy Help Pages

• The TNA has numerous Research Guides pertaining to Courts of Law.
• Many coroners' inquests were subsequently reported in local newspapers  
• The Court of Chivalry 1634-1640 - "The aim of the site is to make available to scholars, researchers, local historians and genealogists the records of the Court of Chivalry during its heyday between 1634 and 1640. Over this period the court dealt with well over a thousand cases of which it has been possible to recover details of 738. These cover a wide variety of topics relating to the social, political and cultural history of the period, from ship money and the Bishops' Wars to pew disputes and duelling, from heralds visitations and grants of arms to brawls in the street and quarrels at race meetings."
• An Introduction to Quarter Sessions Records (archived copy), by Richard Ratcliffe.