The only games I have ever seen any ladys play, where first person shooters.
I have had several ladys on my clans, and they were all FPS.
Reason being, is you can be on a team with others. As many as 8 at once on just your side.
I can't think of any other games online that can have the numbers to be more of a social gathering, than being just a videogame.
Fighting games are all 1 vs 1, untill tomorrows Dead or Alive Ultimate, which I highley recommend.
Offline games, you could try Fable. Thats alot of fun, people say it is too short, but I don't think you are looking for a game that would take many months.
But come Nov 9, the online games will all be empty except Halo2.