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

I looked some figures up on this a year or two for a school project. These figures are from a study totalling names from the 6 Wales telephone directories.

Here are the most common 40 surnames:

1. Jones - 60.57 per thousand
2. Williams - 37.81 per thousand
3. Davies - 36.76 per thousand
4. Evans - 24.66 per thousand
5. Thomas - 22.97 per thousand
6. Roberts - 17.14 per thousand
7. Hughes - 13.38 per thousand
8. Lewis - 12.96 per thousand
9. Morgan - 11.7 per thousand
10. Griffiths - 10.9 per thousand
11. Edwards - 10.33 per thousand
12. Owen - 8.85 per thousand
13. James - 7.66 per thousand
14. Morris - 7.5 per thousand
15. Price - 7.5 per thousand
16. Rees - 7.3 per thousand
17. Phillips - 6.34 per thousand
18. Jenkins - 6.23 per thousand
19. Harris - 5.79 per thousand
20. Lloyd - 5.64 per thousand
21. Richards - 5.51 per thousand
22. Powell - 4.72 per thousand
23. Parry - 4.49 per thousand
24. John - 3.65 per thousand
25. Watkins - 3.39 per thousand
26. Howells - 3.25 per thousand
27. Pritchard - 3.14 per thousand
28. Rogers - 2.71 per thousand
29. Matthews - 2.37 per thousand
30. Rowlands - 2.35 per thousand
31. Humphreys - 2.22 per thousand
32. Pugh - 2.19 per thousand
33. Ellis - 2.17 per thousand
34. Bowen - 2.17 per thousand
35. Hopkins - 2.14 per thousand
36. Martin - 1.91 per thousand
37. Bennett - 1.86 per thousand
38. Bevan - 1.69 per thousand
39. Pearse - 1.65 per thousand
40. Adams - 1.61 per thousand

These top 40 surnames only cover 38% of the welsh population, but this could easily be explained by varying numbers of people per telephone, studies taken from different eras, et cetera.