The Sims and My little pony.

No, seriously, I'm not sure about the whole "game for girls" things. The girls I know, who've been playing videogames, were hooked on AvP, Starcraft, Call of Duty, Baldur's Gate, Vampire the Masquerade (Redemption - that one girl had even made a website about it, in fact), Left4dead, Limbo, etc... Trine was appreciated a lot by a non-gaming girl, too. I also have a friend who's into adventure games almost exclusively and enthousiastically introduced me to Syberia.

The point is : is see no real pattern. And no real "girl/boy tastes" amongst my friends.

You can't go too wrong with The Sims 3 and the two Portal games.

Dunno about number 1, but for number 2 it's easy - hack''n slash RPG, Diablo 2, Sacred, etc.

Since I happen to be female, I'll jump in here. I'm going to assume that your requirements really do fit the personality of the lady you're purchasing for.

Dark Fall: Lights Out (no gore/violence, strong story, one of the main characters is female, puzzles are not as hard as the Myst games). Not a lot of romance, though.

King's Bounty has cartoony violence (you're leading armies around after all), but has a charming art style, light romantic elements, and (if you get the Armored Princess pack that sadly GOG hasn't acquired yet) a female main character.

*edit* If you didn't specifically say "no violence", I would suggest Baldur's Gate I/II, Neverwinter Nights, or Planescape:Torment.

I am just throwing this out there, I make no claims to know what games women like. It's not like I can ever get my wife to play past the first session of anything I buy her. :P Anyway!

The Blackwell Saga is a series of point and click games with a strong female protagonist... Romance, not really? But the lead woman develop a strong friendship with her spirit guide, who is a ghost, who helps her solve the cases.
The first game lacks quite a bit in the story area, and is rather simple, but it is important to the overall story.

Just figured I'd give my input. :)

You can't really place a set of games on the sex of a person. My wife plays everything from Skyrim to Unreal Tournament to Age of Mythology to Words with Friends. Her sister would rather play WoW vs Skyrim but also loves UT, AoM and Words with Friends. I know other girls who would rather play Baulders Gate, then others who LOVE Mortal Combat enough to buy that arcade controller special edition. Then you have the girls who don't play anything but Facebook games. That all sounds just like some guys I know too. :) I think I had a few suggestions in my post. Others that may work are King's Bounty if she turn based strategy and fun graphics like Luned mentioned. The Diablo series, Divine Divinity, Sacred, Dungeon Siege or Spell Force for some hack n slash. Actually, my wife has played through all of those. Trine and Trine II also look good.

Wait, you heard me?!

I envy you Nucklez. :P
My wife is the facebook type.
Just wanted to mention that the Sims 3 is also a great casual game, like others in the thread also recommended. I bought that for my wife, the one game I've bought her that she actually loves playing. :P

Well - don't keep us hanging - does it work ?

Animal Crossing

Baldur's Gate

Yep, I've got several of them to visit me. I love playing Mario Kart with people.

Wow, thanks for the suggestions people.

I forgot to mention that she never played video/computer games before.

What is she into? Being a non-gamer effectively voids most suggestions here, other than P&C games. Even Minecraft may be difficult to get into for a non-gamer, since it may cause motion sickness.

At one time one of my former gfs (shhhhh) and I were working different shifts. We were sending each other letters everday through the Animal Crossing postal system. -___-
You can gift things in that game too.