I'm 14 years old and female.
Games I've played recently:
1. Assassin's Creed 3
2. Bioshock: Infinite
3. Borderlands 2
I'm kind of intimidated because all other gamers here are pretty older than me. Well, here goes.
My first gaming experience was when I was maybe around 5 or 6 when I used to play a lot of Tekken and a lot of other fighting games with my neighbor on her PS2 and my brother introduced me to Runescape (i'm kind of ashamed of this one XD i feel like no one cool plays this and it's a loser game), Age of Empires, Age of Mythology, the first Sims, and Red Alert (I continued to play this until Red Alert 3). Well, now, to be honest, I really like games with a great story and strong characters. Puzzle (like Catherine :3) and strategy games are my forte too. I'm not really adverse to meaningless, casual, random games but I just appreciate a good story. I'm also really into indie horror games like Misao, Mad Father and The Witch's House and games like The Sims 3 and Sim City. I don't mind some killing and shooting either. Adventure games give me a kick, and I've really wanted to get my hands on Tomb Raider. I also play DOTA, Starcraft, Skyrim, Portal, Halo, and some Minecraft (though I suck).
All in all, I play most of the games my brother plays and the games my best guy friend suggests me (I got so mad when he started rubbing Bioshock: Infinite right in my face since he got it earlier than me when he didn't even finish AC III claiming that it wasn't worth his time anymore, the wiener). So I can say, through my own experiences, that females can pretty much play what most guys play if they were really into it.