As a female I like a little bit of everything.
Sims, Final Fantasy, Fallout, Mass Effect, Portal, Mini Ninjas, Jak, Kingdom Hearts, Zak & Wiki, Saints Row, Ico, Shadow of the Colossus, Flower, Devil May Cry, Assassin's Creed, Persona, Skyrim, Loco Roco, Enchanted Arms, Fable, Batman Arkham Asylum, Cooking/Gardening Mama, Dragon Age, Keflings, Harvest Moon, Blue Dragon, Enslaved, Sly Cooper, My Sims, Beyond Good & Evil, Overlord II, Mirror's Edge, Heavy Rain, The Legend of Zelda, Little Big Planet, Prince of Persia, Folklore, Catherine, Pokemon, American Mcgee's Alice, Diner Dash...that's just what I can think off of the top of my head. There's lots more.
But yeah, little bit of everything. I don't knock COD but I personally don't see the lure. I can't stand sport games honestly. And I don't play horror games cause while I LOVE to watch them, playing them just fucks me up.
Hell I know I'll probably get shit for it but I'll even admit that I find games about tending to horses cater to the five year old girl somewhere still inside me.