http://www.myth-weavers.com is a site dedicated to Play-by-Post gaming.
They don't like people advertising games that won't be taking place on their site (so no skype-only games), but there do seem to be many games going on, some for a long while.
http://www.rpol.net/
I don't have any experience with this one, but its another Play-by-Post site with a lot of activity.
I'm not sure where one might find games that run on Skype or other chat servers.