I think most of everyone who has replied to this is going in the wrong direction. There were a lot of games being recommended, however, I think a 'one game fits all' attitude is completely wrong.
If you really want to start someone on games, you have to know something about them. There's so many different play styles that it would be criminal not to consider it.
For people who like puzzle games:
Puzzle Quest - I can't believe no one has mentioned this game yet. It has some of the most basic game play and it's an rpg. I'll give you maybe it's too casual that it wouldn't get them 'into' gaming, but little steps...
Portal - For sure. Did you ever listen to the commentaries? This game was designed to get people to realized what they're getting into. If it's too hard, then... well, FPS isn't the game for them for the next 20 years.
For people with control problems:
Dungeon Keeper II - One of my all time favorite games ever! (Damn you EA for canceling the franchise!) The tutorial on this game is a hand-walking master piece for new players. "Click here and drag here".
There should also be follow up games that you need to consider. Say they loose interest in the first choice. People are going to gawk at my next recommendation.
Metroid Prime I - So, the first part of the level maybe hard. You get access to all of your stuff, and it might be overwhelming. After you beat the first boss, you lose all of it. Thus your controls are now: Aim, Shoot, Jump and Move. The first areas are very forgiving too. OMG IT'S THE GIANT... beetle? takes 3 hits to kill and does about 2% damage... on noes. Another reason I mention this one is that it has a pretty good difficulty curve. You're never given enemies that you can't defeat. After you beat a hard enemy, then you're given some item that makes the older enemies easy. This also means the games about to throw a harder enemy at you as well. That and this game is visually beautiful to a first timer. Down part is that this game can get a little boring or frustrating when you don't know where the **** to go.
If you think they would be into any rpg style game, then give them one from the Mario RPG line. Maybe not the greatest RPG's (I think they're awesome though) but it's great for a beginner no matter what.
People are going to hate this one too, but, Pokemon, the very first Red or Blue game was an amazing game. Easy to catch on to, plenty of stuff to do, and a clear objective to complete.
Alright, criticize away.
~MasterRahl