IMO tomb rider is a bad idea for the uninitiated. I don't know about the anniversary remakes but the originals' controls (and difficulty) are not ideal for someone who's never ever played games. If you want to go that route PoP 2008 is better :P
That being said, yesterday night i decided to have a look at to the moon, you know, just for 5 minutes before i go to sleep. Ended up playing it till 4.20 am. And I think it's perfect for your purpose. The focus is on drama and romance and is more of an interactive story than a game, while still having characters walk and search (unlike in visual novels, so she'll get a feel for the movement), and an easy puzzle minigame. IMO it is impossible for anyone who even remotely likes stories to put it down/give up/leave it unfinished, especially because of the way it is told. I'm going to use it myself to change people's minds about games.
IMO if she likes fantasy - tlj, if not - to the moon.
btw have you considered dating sims? :D
Zolgar: If your girlfriend doesn't like video games, don't try to 'convert' her.
Have a meaningful conversation with her about her feelings of video games, as opposed to your own. Explain to her that while she may feel that they are a 'waste of time', entertainment is never a 'waste of time' (unless you're doing it instead of something you should be, then it's all miss-spent time).
Pose to her that the video game industry is just like the movie or book industries, there are strong games with solid plots and characters you can fall in love with.. and there are games that are mindless fluff.
I see nothing wrong with an attempt at 'converting'. I have the impression that you think of it in a manner that is too serious ('changing someone' are harsh words imo), and possibly perceive it as something that is...forcefully imposed?
When it comes to all kinds of entertainment, all the prejudice stems from lack of exposure (aka ignorance) and culturally imposed opinions. I give things I like to my friends all the time(even people I have just met if we have similar interests, i'm extremely geeky :P), provided it's something they want, or I conclude that it's something they might enjoy. That includes games, 'exotic' or 'normal' movies, books, music, tv shows, comics, pretty much everything. By doing so I am not changing them to suit me or whatever one might assume, but simply providing them entertainment, relaxation, and at the same time often making them more open-minded, aware and possibly educated. And i do believe that everything mentioned enriches one's life. Of course, it's bad when you forcefully try to impose it with no patience.
Red_Avatar: Sadly enough, the huge majority of girls here prefer those horrible horrible and crappy Facebook games.
At my last job, I tried to "convert" a girl who had had a Playstation as a kid to try some adventure games and a few other games that I thought she would enjoy. Didn't work - not even a bit. However, when she got introduced to Facebook games by a friend, she spent loads of time on Farmville *facepalms*.
That's the moment I gave up on trying to "convert" girls - any girl is already going to have been subjected to games many times before and the chance of anything you suggest appealing to them, is pretty low. Even such games as Beyond Good & Evil or other games with strong female leads.
Did you play the nostalgia card? As in games similar to the ones she used to play?
Also, I think I'm in the minority, but I don't think adventure games are that good for non-gamers by default. At least the older ones, depending on the person (which is where you must be a good judge of character I suppose), might be too slow and way, way too frustrating. Unless they play it with a walkthrough. The newer, more casual ones are better for that purpose.
i think that facebook games show that people generally prefer faster gratification. I usually start with casual games - peggle, bejeweled (btw am I the only one who *really* dislikes bejeweled-like match3 games?), bookworm adventures, 4 elements, plants vs zombies, auditorium, world of goo, jolly rover. These games change people's bias , make the perfect foundation and show where you might go next. Then you can go with puzzle quest, cogs, toki tori, amanita games, macguffin's curse, glowfish (a wonderful casual underwater platformer btw :)), aquaria, and various adventure games such as telltale games, original monkey islands, broken swords etc. And then to more complex games. The most important thing is to do it *gradually*.
Of course with people who love stories and read a lot, the correct route would be adventures (harder ones if they like logical puzzles) and easy rpgs (visual novels too of course, but i haven't 'played' any).
Btw as much as I ADORE beyond good and evil, and would gladly try to make everyone play it, those fighting sequences in the water are not for newcomers. But then again, I might be underestimating people, and of course, again it depends on the person. I have a female friend who played only captain claw and tarzan (that 2.5d psx/pc platformer) when she was younger, and then later she played psychonauts (she's a geek for psychology), and to this day psychonauts is her fav game. She didn't finish the final stage, but was persistent enough with everything else.