These games are actually some of my favourites. Their mechanics are simple enough, but the games have enough depth to keep you coming back to play again. Intro games are easy enough that anyone, even people whose board gaming experience stops at monopoly can play, the trick is that Intro games leave you wanting to play again and again this means they are great for introducing people to the gaming hobby. Some also work as a fantastic 'bridge' to more complicated games and are good for moving a new gamer to the next level, to find out which intro game is best for you read the individual reviews.
Alien Frontiers - This is one of my favourite Intro games out there, Alien Frontiers introduces worker placement to players in an awesome theme and in a slightly less overwhelming atmosphere, what I mean is because of the randomness that comes with rolling dice (your workers) your options are limited to a few choices based on the results of your roll.
Carcassone - An all time classic intro, Carcassone introduces some staple mechanics of modern board gaming, if you are trying to get someone into board gaming, this isn't a bad place to start.
Kingdom Builder - 2012's game of the year because of its accessibility, personally I would not 'introduce' someone with Kingdom Builder but that is because although I appreciate the game, I am not enthusiastic about it and if you are the one showing a game, you need that enthusiasm. On the other hand, shortish play time, simple rules make for an extremely tactical game that can teach many things about modern board games.
Wilderness - I like Wilderness as an intro game for a few reasons, mainly its off the beaten track and I find slightly more intriguing than train games and the like. I really like Wilderness' ability to introduce players to 'cards' there are multiple types, some that happen every turn, some to boost your own capabilities, some to hinder your opponents, there are also different ways of tracking the lasting effects of these cards. Lots of games have strong card components and I find that newer players tend to stay away from the card / text heavy games, Wilderness should help make these more accessible.
Lords of Waterdeep - Lords of Waterdeep is yet another worker placement game, the reason I find it works so well as an intro is because the game play starts quick and easy and turns into a strategic web of trying to decipher how to score the most points with every move. By giving access to an additional worker half way, and allowing player's the ability to construct more usable buildings LoW evolves into a more intense game but at a perfect speed to ensure everyone understands what is happening. By the time you get to your second game turns whip by in no time.
Rondo - To me Rondo makes an excellent intro game, although I haven't owned my copy for very long at all I have already shown it to at least 10 people and they all were left with the most important impression from an intro game: wanting to play again.
Safranito: - This is my personal go to game when introducing anyone to board games, the mechanics are so fantastic, it is by far the best combination of strategy and dexterity in any board game. Rules are simple enough to get hooked on though.
Augustus: - Even though simultaneous game play is not the best for introducing people to board games, Augustus offers simple rules, quick setup / play time, and the desire to play again after. As an intro game Augustus teaches mechanics that are common in other modern games.