Stick with games with relatively simple controls, and not requiring too much finesse with the dual analog sticks, and without having to deal with to much manipulation of stuff in 3d space. In short, expect her to have trouble with realistic-esque driving games, platformers, FPS games that don't have a very good aim assist. Portal for example is right out.
As well keep her away from hardcore-esque games. Highly realistic graphics, complex lengthily plots or "deep" characters won't be the main focus of her enjoyment. Instead go with games that focus on the game it's self. Solid level design that's fun to play through, gameplay that focuses on one or two mechanics that are easy to work with and fun to use, an art design that's please to the eye, and for the love of god COLOURS!
Personal Suggestion: Kingdom Hearts. For all of the above reasoning, plus Disney characters.
Fanta Grape said:
But if you don't feel like giving her a year's worth of gaming to try out, just start off with Final Fantasy VII. Everyone loves Final Fantasy VII.
[DO NOT REPLY TO THIS STATEMENT]
I'm replying to this because OH GOD NO. A dense plot filled who's basic motifs that have been done and done again in the current age of nigh militant environmentalism, rather boring characters, the graphics have aged horribly, the entire start of the game is very dull and confined, both in plotting and the look and feel. Then there's the game mechanics, the fights themselves are repetitive, most of the enjoyment there coming from your dealing with a massive amount of information, none of which she'll have any real context for, or experience with.
Any final fantasy game, or for that mater any game that delves to deeply into RPG stats and mechanics, is a Bad Idea.