Specter Von Baren said:
It really depends on the person.
This is really a huge factor. Personally I wouldn't start anyone off with motion controls (and I'm biased here) because I don't think its the best demonstration of what gaming has to offer anyone. Ever. I might recommend something with Co-Op, just so you and the other person are on a team and they feel a little more comfortable playing. Maybe a racing game that has bots in it so they don't feel bad if they lose to you. My first video game ever was Lego Racers. It wasn't too fast paced and there wasn't too much going on at once. Obviously that's a game from the late 90's so its probably out of the question. But pick something that doesn't have too much going on.
For fighting games, I really can't say as I don't have much experience with it, but I might say Super Smash Brothers. Really any of them would do. There's bots of varying difficulty, teams etc so the person isn't just always alone. It's one of those easy to learn, had to master games I've found.
If you want to introduce the person to shooting games/the mechanics of shooting games I would recommend Timesplitters: Future Perfect. Its really fast paced BUT, you can turn off bots, custom make your own maps to train the person in the ways of walking around, looking around, shooting etc, pick weapons that are good for starters, it has co-op and before you introduce someone to the actual combat there is a game mode that doesn't involve shooting at all. Just running away from other players or chasing them, letting them get more used to moving around. Then you can introduce them to game modes when they're defending an objective from an enemy (they won't have to move and shoot much) and eventually work them up to regular team death matches or free for alls. I found it to be an amazing game to show my friend, who hates fps games and never plays them, that they aren't all bad. He actually found it to be easy to learn and fun to play, even when losing because of the good, funny nature of the game. I even taught an 11 year old to play it.
EDIT: thinking of it now, Portal would make sense because its not too complicated in terms of mechanics and can demonstrate some good story telling. Like I said though, it depends on the person and what you want to first introduce them to.