Here's how I managed it, in exactly five games.
Total. Flippin'. Conversion.
The first move: she was sassy, with a good singing voice, so... Sing Star: Motown, in a party setting, worked like a charm. This led to more Wii-based entertainment, in the form of Rock Band. During lulls, where voices needed resting, etc., a quick switch to Cave Story, in order to (re*)acquaint her with classing D-pad/2-button controls in an engaging and fun manner. Step up the level to multiplayer New Super Mario Bros., and after realising she spent over nine hours gaming, I realised I had seen the face of a new-born addict after their first hit. It was like a Disneyfied version of Trainspotting.
The final game, to introduce her to a more current, three-dimensional world for her to get used to: Okami.
Anyway, if there is one genre that will pique the interest of... pretty much anyone, it has to be puzzle-solvers. Mystery solving is the great leveller of humanity, as you don't need to be good at games to become immersed in puzzle-solvers; you just have to apply your noggin. Which anyone with a noggin can do. So, for that, I would say
[ul]Professor Layton & the thingiest thingumy
The 7th Guest/11th Hour
Black Mirror series
City of Secrets
The Last Express[/ul]
*As no matter how little experience one has had with vidjagames, everyone in the developed world has played Super Mario Bros. at some point in their lives.