My daughter likes most games as long as I'm willing to play with her. She dislikes excessive gore/violence (but has a good threshold anyway... she can watch me play Left 4 Dead 2 even though she finds it scary).

She likes relaxing sandbox games such as "Tiny Glade", story/puzzle oriented games like "Planet of Lana" or "Cocoon", racing games like Mario Kart 8 and Need For Speed (she's awful at it, but she likes it), platformers like "Princess Peach: Showtime!", and will gladly watch me play Space Marine or even help me with XCOM Enemy Unknown (by pointing out enemies). We're currently having a hoot playing "It Takes Two", which is a coop split-screen puzzle platformer.

I think pretty much her only requirements are: "not too scary" and "I can play next to daddy". That's it. Not necessarily just "Girl Games".

One thing I discovered with her is that we both have very low tolerance for "talkie" games with lots of cutscenes where you must skip through all the pointless dialogue. They are very kid-unfriendly (kids want to just play the game and read very slowly anyway, if they can read at all) and, if I'm being honest, also adult-unfriendly. Most games have crap storylines anyway, just give us the gameplay and imply the larger plot briefly, much like Planet of Lana does.