I actually got into gaming through Pokémon, so I'd recommend that, starting with first gen. As the series went on, it got more complicated, so it'd be best to start off with something simple.
Portal's also great due to the fact that it requires thinking skills rather than gaming experience.
Kirby is excellent due to overall low difficulty and attractive art style.
Old platformers like Mario and Sonic are alright because of their simplicity, though I'm not a big fan of them.
Mario Party seems to be good for introducing others to games; it's a social experience with a bunch of simple mini-games with good variety.
Or you could try something with a good story. Think of what she likes and then go from there. Just try not to pick out anything too difficult; Persona 4, for example, may have a good story, but it can be a bit difficult at times *cough*ShadowYukiko*cough*.
The problem with my suggestions is that none, except Portal, are PC games. Pokémon's easy to emulate, but y'know, who does that? If you must use a controller, I'd recommend things that require little from one's reaction time or knowledge of a controller. Once again, Pokémon's great like that.