My mom and dad both used to be pretty big into SMB3 and SMW in the early to mid 90s, and I wasn't interested in playing them at all until probably around '94 or '95. I loved Mario is Missing, solely because I liked Luigi better than Mario, but since we didn't own it and had never found it in stores, we kept renting it.
One day while we were at the rental place, I saw SMRPG. I had no idea what an RPG was, but this was Mario and looked really cool, so we got it. I had no idea what was going on when I played it, but I still liked it, and it was even better when I started figuring it out. My mom, however, had so much fun with it that she went out and bought it. We raced to see who would finish the game first, and she won. I still remember her excitedly coming downstairs to tell me she had beaten it, and it went by too fast for her to call me up to watch it. I finally finished it a little later.
Around 2000, I finally got an N64. My mom was so confused by the three-pronged controller and overwhelmed by the 3D graphics, and I was so anxious to play it myself all day, that this was about the time she fell out of gaming.
In 2003, I got Superstar Saga, and on a whim, asked her if she wanted to play it. She didn't finish it quite as quickly as SMRPG (probably because the GBA was in my pocket more often), but she had a lot of fun with it and was pretty good at it. Unfortunately, the Bowletta fight proved to be too huge of a jump in difficulty from the rest of the game, and she never finished. (Also, one time I accidentally erased her file, and so surreptitiously played the game through to the same spot she was at in the same amount of time. But I ended up telling her anyway.)
Then in early 2007, we finally managed to pick up a Wii. They both played Wii Sports on the first day, with the rest of the family, and both found it rather intuitive and fun. Dad stayed there, usually playing golf or bowling, but also being a fill-in player when one or more of my little siblings wants to play something. Mom started gradually moving on to other games, starting with Excite Truck, which is still one of her favorite games to this day, then Elebits, which she is better at than me, and then Sonic and the Secret Rings... which didn't take as well as the others. And then Lego Star Wars, which, in addition to being a fun and hilarious game, was a good, risk-free way for her to practice moving in 3D, since you can never die.
Later in 2007, we got Mario Galaxy, and as soon as I could pry myself away from it, I had her start a file, and we played in Co-Star mode. We got three stars that first time, and once she learned to do the basic moves, I never had to do Co-Star with her again. Now she has about 100 stars, and is determined to get all of them.
Just a few days ago, she started playing Twilight Princess. She admitted that she wouldn't have been able to play it a year ago, but Galaxy, Lego Star Wars, and Elebits were gateway drugs. She's having a lot of fun with it so far, though she realizes in hindsight that it's kind of weird for Link to have a girl's name. Meanwhile, my dad just started playing Wii Fit today, and really likes it. His center of balance is pretty good, but when he does the Tree pose, he can't stay up on his left.