Like Icelandic Surnames, Wales has a history of patronymic naming. The practice died out in the early 17th century in urban areas, and up to the early 19th century in outlying rural areas.

95% of the Welsh population are covered by only 39 surnames.

There are four common classes of Welsh surname:
  1. Straight Patronym - These come from the name of the father, with an s appended. Examples include Jones, Williams, Evans.
  2. 'Son of' - Like the Gaelic Mac or Mc, Welsh used ap to mean son of. "John ap Richard" is John, son of Richard. This developed to Pritchard. Further examples include Bowen (ap Owen) and Pugh (ap Huw).
  3. Purely Celtic names - Often describing the person, their occupation, or a place. Examples are Lloyd, Llewelyn.
  4. Imported English names.
The practice died out as wealthy and stylish families began to carry their surname to future generations. This is, of course, a minor nightmare for genealogists with Welsh ancestors.

Sources:
http://www.data-wales.co.uk/names.htm
http://www.melcombe.freeserve.co.uk/helps/patronym.htm