Two women here. My girlfriend and I play games quite a bit, so I shall do my best to answer for the both of us.
What three games have you played and enjoyed lately?
Myself:
1) Resident Evil 6: I've played so much of this over the past few days it's ridiculous. Finish off Piers and a quick play of Sherry and then I'm done, I swear - likely much to the delight of the girlfriend. She doesn't like games with any kind of horror of jump scare moments at all.
2) Various Pokemon Games, from FireRed to Ruby and Sapphire to Pearl to White. Ahh, nostalgia.
3) Skyrim. I love this game. Free-roaming RPGs set in a time long past are one of my favourite types of games.
Girlfriend:
1) Minecraft: She loves building elaborate creations, and creating maps for us to play through together.
2) Vampire the Masquerade: Bloodlines. Awesome game. Doesn't like the horror elements, but loves the game for what it is.
3) Saints Row The Third: Another awesome game.
We usually play COD and Tekken with each other regularly as well.
What is most important for you to enjoy a game?
I like playing all kings of games. There isn't a particular genre that I don't like. What's usually important in most games is a good story (if it is meant to have one), a decent leveling system (if it has one), fluid and intuitive controls, and good aesthetics. And then there's the little things, like if it's an RPG I want to be able to develop my character and alter their stats and appearance as I see fit. If it's Survival Horror/Horror/meant to be scary, I want to feel scared and tense. Etc. Ultimately, whatever the game is trying to bring to it's audience, I enjoy when it's done well.
For my girlfriend,, it's mostly about customising her character and the story that she's following. With this in mind, she mostly like RPGs, MMOs, and whatever genre the Sims games come under (Simulators?).
I don't see the games we play any different from any other female gamers, or any male gamers. Everyone has their own tastes, regardless of gender - even if some games are marketed at a specific one.