I wouldn't poison their mind and turn them into a graphix whore. I'd give them (in this order) :

1. Zelda OOT
2. Mgs1
3. Chrono Cross
4. FF VII
5. Shadow of the Collosus

I would simply give have them play the classics

FPS: Half Life 2 (PC)
RTS: Starcraft (PC)
RPG: Final Fantasy VI (SNES)
Platforming: Mario Bros 3 (NES)
Adventure: The Legend of Zelda: Ocarina of Time (N64)

Probably start him with the HL2, because it is somewhat recent, then move him to Starcraft and then backwards per generation from there.

no more heros
Okami
Super Smash Bros. Brawl
Final Fantasy XII
Pokémon Diamond & Pearl

I will start that person with Wii Sports. Get them having fun, then I'll move up to Mario Kart Wii.

Once they really get interested I'll throw in a Single player game like Galaxy, and then the awesomeness of Chrono Trigger, for their RPG taste.

I'm not sure what the last one would be... probably Shadpw of the Colossus, that would blow them away and shit!

I'm serious, if you have a person that has never played a game before, you have to start with Wii Sports. The game is about getting new people into gaming, anyways.

I would show them MGS3, Pokemon Diamond, Resident Evil 4, Uncharted and Kilzone 2!

Damn, forgot Flower - great choice there.  I'd still show them LBP over SMG, simply based on the different rections of non-gamers to both (I have both) I know that despite how good SMG is they go ga-ga over LBP, particularly when you knock together a crazy car in 1 minute in create mode and let them try out dressing up Sackboy.

1. Wii Sports.
2. Elektroplankton.
3. Katamari Damacy.
4. SimCity.
5. Portal.

1. First they get to create a Mii and then try all 5 sports and their training modes. Seeing how the controller works usually breaks down their skepticism. Everybody I've shown this game to has been hooked immediately, including non-gamers, relapsed gamers, hardcore gamers, casual gamers, and my parents. This part could last hours.
2. Then they get to play around with 10 "non-gaming" audio-visual interactive art experiments, to see that not all games are about winning or even keeping score. Everybody I've shown this game to has also been hooked immediately.
3. Then they get into a game with a story, and get the best story in gaming, the best intro in gaming, the best music in gaming, and some of the most unique gameplay. Any non-gamer I've shown Katamari has fallen in love with the art, the music, and the concept. They either want to play all day or they want to watch me play all day. I'd show them the controls and then hand them the controller and count the smiles. Then I'd go on YouTube and show them that one commercial that was inspired by Katamari, to show them how gaming is inspiring other art mediums.
4. Then SimCity would ramp up the complexity and difficulty a little, while still being accessible. I'd hang out and offer advice when they asked, and see how long they stay interested in their first session.
5. Then I would introduce them to a game with a comedy/horror plot, the best shooter/puzzle/platformer mechanic, and an unreliable narrator. This would show them that a game can tell a story without cutscenes or dialogue, but just with hearing the narrator/host of the game and finding clues in the environment as you explore (the cake is a lie, etc.). I think it's important they don't have to sit through cutscenes in their first gaming session, but get to play the whole time. Their gaming session would end with the GlaDOS battle and they would be rewarded with a song. I think it's important that they be rewarded with a song at the end of the day. Then they would be a gamer.

Explanation of my curating as a whole: None of these games give you weapons, and none are about destroying. I think the typical skeptic thinks all games are about shooting bad guys or saving princesses from monsters. That would be one of the concepts I'd be fighting with my "game curating." Wii Sports is a collection of games that they'd be familiar with from real life, the next 3 games are about creating (music first, then planets in a comical way, then a city in a serious way), and then Portal would teach them first-person controls in a 3-D environment, but without all the guns and violence and macho space marines. Also, the first 3 games barely use buttons, but slightly get more complex than the last. Wii Sports Tennis and Boxing would be first, with no buttons. Elektroplankton is played entirely with the touch screen and mic, but with the D-Pad used to change a few things while you play, but it still doesn't require precision yet. Katamari is just bliss and you just need 2 joysticks. Then they get a game that's about management and menus, and then at the end they finally get a game that requires aiming and timing. I'm assuming they've never played a game in their life.

It hurt to not put Tetris, Dr. Mario, or Galaxy in there. It really did. Hopefully they would be converted with my 5 choices, and then I'd send them home with Tetris and Super Mario All-Stars.

And I can't believe how many of you are mentioning RPGs. I'd at least start them off with a platforming RPG like E.V.O. or Super Paper Mario, or an action RPG like Secret of Mana. I think too many menu screens that take you out of the game world might... take them out of the game world.

Some of you seem to think f you show a non-gamer graphic intensive games they will instantly go ga-ga over the game. Trust me that is just not the case what so ever. Its all about familiarity and comfort with the controls. Hence why wii sports is so successful at drawing people into gaming for the very first time. MGS4 will have 99% of people asleep in a couple minutes. They won't know if their playing a game or a b-movie. And don't even think about showing them an RPG unless its name starts with pokemon and their under the age of 13.

Uncharted
Call Of Duty 4
LBP
Resident Evil 5
Max Payne 2

@Rubang: I believe you're almost absolutely right on the money with your list. Except for SimCity. I can almost see someone getting into Portal, but SimCity requires too much commitment.
And also, you're so right about the RPG thing. People who are saying Zelda are absolutely insane as well. Have you never met a non-gamer? Accessibility is key here, people.