Girl gamer (?)
 

Try Sims........

Maybe Spore :p

I know it's not Rpg, but I would recommend the Silent Hill series if you like horror games. It's a great storyline abd feel so sucked into it. I guess both genders would find it cool, because I've seen girls play it :)

Silent Hill 2 trailer: YouTube - Silent Hill 2 Trailer
it's said to be the best on in the series :3

A Rpg girls would like is Neosteam, it's free to play ;)

I say you should just go and browse a video game store and see what interests you.
I'm a girl and I'm a hardcore gamer. You shouldn't start by asking what games girls like because they aren't always (read: usually) very fun! I do like some 'girl' games, like Sims, but I like many more 'non-girl' games too.

Just go out there and get started! :3

I'm a girl gamer, and all I play is drifting games, other car games, shooting, and violence. I love it. Thats kind of a secret though.
I also like final fantasy games.

I recommend Zelda. Anything Zelda.
Zelda is more aimed towards puzzles, but it has enough action and fighting in it to keep you interested and to keep the games fast paced. The storylines are interesting, and you can easily fall in love with it. They're usually pretty challenging, though, but they become easier once you get the hang of it (the more you play it, the more you know what to look for and what you should be doing).

I generally would recomend not to ask what games you could like as a girl, the fist answer will be Sims in that case, everywhere.
All gaming girl I know are playing exact the same things as the boys, of cause many girls play Sims, but you seriously can't call that gaming in my oppinion

You just have to try some games, then you get an image of what the different genres are like. Oh and do you want to play with a pc or a console?, thats the most important point out of my view

flower.

best way is to list what types of stories you like.