I found some of my Welsh roots and am writing here to say where I got them, in case this helps someone else. (and I helped make this site but wasn't actually sure I had any Welsh!)
As a disclosure, I have two Pilgrim ancestors so that makes this much easier, as there's a lot of research done by others and posted online on everyone who was on the Mayflower or came shortly thereafter. If you've got a famous ancestor, many times you can just google their name and the word "genealogy" and up will come lots of great starts. Even if you don't, just try googling your ancestors' names, the towns they were born in and the year.
So I got to my Morgans through googling Elizabeth Witter, who had married a descendant of William Brewster. The Brewster line was all done, as far back as it can be reliably documented and I was going and trying to find people who had married my Brewster ancestors and found Elizabeth Witter's father was a Joseph Morgan. I googled his name, birthdate and town and I found some work done on him by someone else which included his father's name and birth year and birthplace, Tredegar, Wales, so I googled him and found a long list of his family that went back to Morgan ap Llewelyn, born about 1330, in Tredegar, Monmouth, Wales. All that wonderful work was done by someone else and you can see it here at:
http://www.angelfire.com/folk/morgan/fam/fam04144.htm
So now I'll come forward and start working my way backward, looking for the source documents.