Worms: Armageddon. You can play it with her as well
I'd also recommend old point and click games.
Siberya is probably a perfect choice actually, female protagonist, cool story, emotional, controls are obviously simple as hell and no time puzzles as far as I can remember. If she likes the genre, there's also the Broken Sword series, she might be into that as well if she likes mysteries.
Bastion also comes to mind, it's relatively easy to play as well (not 100% sure if it's for an absolute beginner though), just tell her not to use the temple stones. Something a bit more meatier... maybe she'd like Civilization? There's not really much there that she needs previous game knowledge for and she can take her sweet time as it's a turn-based game. It's a daunting choice, but to be fair, not much more so than it would be for 90% of the gamers trying it for the first time, so she's not at a disadvantage there.
Plenty of options out there, just try and think of stuff you know of that's not too twitchy, has timed missions and such. Anything she can take her time on and get to know the game before it flies before her eyes and drops a GAME OVER screen on her is a good choice. I'd imagine going with less violent stuff would be a plus as well and something with a heavier emphasis on the story (and obviously have it be a good one).
Also try and keep what genre she might like in mind - just think of what kind of books/movies she likes and whether she wants to just relax with games or throw in a bit of a mental challenge.
PS
Oh. And
Portal, particularly the second one. Yes, I'm aware the first is better, but the second is a better choice for someone new to gaming, speaking from experience on this.