As the resident GM of my group, I generally like to meet prospective new players one-on-one first before I extend an invitation to them to join the group. The main reason for this is because we host the game at another friend's house and I don't feel comfortable inviting people to someone else's house unless I have at least gotten a feel for the person.
Though we don't discriminate in our player selection, I tend to look for mature (generally meaning over 18) players for reasons which should be fairly obvious.
Typicall, the players in my group are friends on a level outside the game. That is, we do things other than play RPGs together and we interact with each other inbetween game days. Recently, however, we were looking to expand our player base, and so I actively put out a call on these boards, looking for interested gamers in the area and have thus added several gamers who I don't yet know on deeper level.
I have had much greater luck contacting other players since the discovery of this website. I also happen to be registered on www.accessdenied.net, but had very little success with that site, and very little success finding gamers in other venues. Penandpapergames.com has been a real boon in helping add players to our mix.