A common descriptor in hobby parlance is "gateway game," meaning a game that takes people who supposedly do not enjoy board games and introduces them to fun board games with the ubiquitous Important Decisions. Like Lucy in The Lion, the Witch and the Wardrobe, non-gamers, using the gateway game, step into a whole new world. Expressions of gratitude, followed by, "I never knew such a thing existed!" are common. But here's today's question: how many gateway games are necessary for a gamer's collection? Answer in the comments!
"Gateway game" is kind of a hard term to pin down, as really, any game can serve as a gateway if that's the game that draws someone in. Dominion, while I don't consider it a truly gateway game, has nevertheless scored a hit with virtually every player I've played with, gamer or not. But by gateway, I mean a game whose rules that are almost intuitive (they can be fully explained and understood in 5-10 minutes tops), that plays in less than an hour, and that has heavy player interaction (whether this is produced by the game or is layered over by the players, and by interaction I don't mean a take-that element).
I've mentioned elsewhere that Ticket to Ride is my ideal gateway game. It's the one I use most frequently to introduce new players to hobby gaming, and I still find it tremendously fun every time I play it, whether new gamers are at the table or not, a rare achievement for a gateway. I also own several games that fall more into the party category—very short games that can accommodate lots of players but that still have Interesting Decisions to make (I think For Sale, Incan Gold, Money, etc., fall into this category)—and Settlers of Catan (though I don't use this as a gateway game very much, mostly because I'm burned out on it).
Generally, though, I don't keep many gateway games about. The reason for this is twofold: first, most of the people in my circle have already stepped through "the gateway." I've been playing games—hobby or otherwise—with my family for years, and that's usually their activity of choice when we get together. It's true that they're usually not interested in trying Troyes or Through the Ages, but they usually like something a little meatier than the standard "gateway" fare. Same with my friends. And second, gateway games have a tendency to get stale quickly. The short playtime and almost candy goodness of them limits my palate for them. Pudding is good; not for every meal.
Different games appeal to different players, so I can understand why some gamers want the ideal gateway game for each player that comes to their table. For me, I can usually find something among what I already have that will appeal to almost anyone. I choose to allocate my gaming dollars toward games for players on the other side of the wardrobe.
I've been working very hard to bring my family into the realm of boardgaming. It can be tough sometimes - my parents are pretty old and often get tripped up on some basic elements. When I introduce a new game I field a lot of questions. Some games have flopped, some games were appreciated more than I expected.
My family's current favorite is Ticket to Ride. It really is an ideal gateway game, since the rules are so simple and it has a familiar mechanic (set collection aka rummi). Kill Dr. Lucky is also pretty popular, although you can't play that one too often as the strongest point of that game is the humor which would get stale if you played it every week.
Carcassonne is generally pretty simple and a good gateway- though better introduced in a group rather than 1-on-1 since a newbie will get schooled almost definitely.
Eruption serves as an excellent gateway game as well. It's not as simple as Ticket to Ride but the game progression adds in the complexity over time. I also like it because it's a game in which the other players can gang up on me (which they do since I'm the gamer and they assume I automatically win everything), which steps up the complexity of my game first, which allows me to demonstrate the cool things you can do if you fall behind. And then it's not hard to catch back up.
The important thing to me is to keep stepping up the complexity of the games I introduce, bit by bit. As new gamers learn more and more games, they become more familiar with gaming-specific terms and concepts, and the next level game becomes easier to explain. Cooperative games are especially useful with the stepping-up process, since you can clearly explain what needs to be done without sabotaging the game by giving away yours or anyone elses strategy. The newbies also don't need to worry about you creaming them since you're on their team. Pandemic in particular introduced my family to a whole lot of concepts, and I was surprised how well they handled Kingsburg, even asking to play it again. I'm hoping to step them into Shadows over Camelot soon, and perhaps, someday, eventually... Cosmic Encounter, which would be a blast to play with my family.