I think that to introduce somebody to gaming, it doesn't have to be an overly complex game, much less a hard game and as contradictory of my philosophy to gaming as this may sound, it needs great (or decent) graphics and if it's story driven, it needs to start with a bang.
Also, bare in mind that we can't pick any game, we can't give them Planescape Torment or Baldur's Gate, because they'd be simply too overwhelmed by the complex mechanics and the sheer amount of gameplay options those games offer, at least, not yet, until they become a bit more familiarized with games.
Just as Yahtzee said, we're taking baby steps here, we're not giving a motorcycle to someone who doesn't even know how to ride a bicycle, nor we're showing Citizen Kane right away to someone who just started to watch movies.
My 5 gaming introduction picks are, in no special order:
-Angry Birds: Yes, I know this isn't one of the best games ever made, but this list is not "our favorite games ever" or "best games ever", this list is about "gaming introduction". Okay, Angry Birds, it can be either the iOS version or the Chrome version (wich is free and available to pretty much any PC or laptop). The game's controls are simple enough, with charming graphics and you can see stuff being blown to pieces without too much effort and it also has a great difficulty curve.
-Mass Effect 2: Yes, I said Mass Effect 2, not the first game, at least, not yet. I said that we need a story driven game with a great start and I'm hard pressed to find a better game with an equally great introduction (except maybe BioShock), also, say whatever you want about the game, it still has a great combat mechanic that's simple enough for a beginner to understand and the conversations are quite entertaining too, to say the least.
-Mario Kart Wii: It can be pretty much any Mario Kart, but I picked the Wii iteration simply because it's the newest and the easiest to find. Also, the Wii version introduced the "Steering wheel" configuration that's incredibly annoying and stupid for hardcore fans, but incredibly easy and entertaining for a beginner. I know, from my experience, that this game series can do wonders to introduce almost any non-gamer to gaming and Mario Kart Wii continues that trend. Speaking of wich...
-Wii Sports Resort: It's no secret that the Wii introduced many people to gaming and Wii Sports did wonders to reach that goal, but the controller still had it's limitations when people started to notice them. Enter Wii Sports Resort, thanks to the Motion Plus addon, the controller can pick even subtler moves and almost every single minigame that was included with the original Wii Sports was included in an updated form. Annoyied by the golf game not picking your movements?, Resort had that issue addressed, but not only that, it introduced a myrad of other great minigames.
-Mario & Luigi: Bowser's Inside Story: I can't praise this game enough, with amazing graphics that surpass almost anything ever seen for the NDS, a hilarious story and great combat mechanics that are simple enough to pretty much anyone to understand, there can't be a better game to introduce anyone to RPGs and Mario's universe.
So that's it, my Top 5 pick of games that are great for beginners, I was tempted to add Half-Life 2, Portal, BioShock and even Super Mario 64 or Super Mario Galaxy, but, as I said above, baby steps first, then you can gradually introduce other, better games to them.