A good friend of mine is going through this exact thing right now. I had to intercede. He was trying to get his fiance to play Police Quest of all things. He needed serious help.
Things that worked with her:
--Wii games, specifically, Wii Sports. The movements are natural. The games are easy. Anyone can pick up Wii Bowling and get into it quickly. Trust me. I got a room full of librarians, many who were 50 and up, into playing video games with this goofy ass bowling game. (If you are wondering why I did this, I did a little workshop on why video games were appropriate for libraries to have alongside books, videos and music. It worked.)
--Games with really simple controls. I saw a couple people mention this. But if you have a game that only requires one or two buttons, like Little Big Planet, it makes it easy to get the basics of gaming down.
--Games with infinite lives. No one likes to die. It sucks. Starting all over is annoying.
I'm going to have to disagree with RPGs. As someone who got into RPGs later in gaming, when I first saw the inventory management involved, and some of the complicated leveling systems, I was overwhelmed. Although the battles are slower, until you get used to the incredible amount of minutia some of these games employ, it can seem a little boring. And Game overy.
And the Sonic thing, yeah I can see that. The first time I played that game I was like, "Shit! Why is everything going so fast?!" If I had never gamed I would probably think people who gamed had genetically engineered reflexes or something. That game can be really crazy looking to someone who hasn't gamed.