I don’t know if the others are “gamers” so, here’s my list of “go-to” gateway games.
Pandemic - As much as hard core gamers don’t particularly like this one, it’s an excellent introductory game and has a way of pulling people in to try more stuff. It’s a bit more cerebral than your apples to apples type of game, but it’s casual and the important bit is this: If your group has don’t like to lose issues then this is great because everyone wins or everyone loses. I pull it out for mostly non-competitive groups.
Bananagrams - It’s a fast pace don’t memorize the dictionary scrabble. Again, caters a bit towards those who like to think; but, it’s pretty darn approachable. I can’t use it much in my groups because there’s a lot of people who don’t speak english as their native tongue, and so word games are out. But, in any other group it’s an easy way to break the ice and your only opponent is yourself for most of the game. Making it squeak into that competitive, but not competitive sweet spot.
Dix-It - Already named here. I just want to call attention to it. It’s a pretty simple game, but it relies a bit on imagination. If you aren’t with creative types it might not go over well; but, it’s always worth a try. You want to pay special attention to the art pack you buy, though. There’s higher and lower quality art for the game.
Ticket To Ride - Again, a game that isn’t wholly accepted by the gamer movement; but, if you like a teensy bit of strategy this delivers without being overly complex. It’s a shut up & sit down type of game, rules can be explained in less than 10 minutes, usually about 5. Biggest problem with this game is that if you get to be too good at it, there’s a pretty big score differential. I sometimes throw games of this because it is good at getting people hooked and I understand getting other people to win some games is important to making them like them.
Dominion - This one is risky. Either your group will love it or hate it. There’s a combo engine component to the game and that’s usually the divide. There’s also some attacking going on here. And worse, there’s no easy predictor for whether a person will love or hate the game. I just know it hooks some people. I pull it out eventually with every group and it either stays in the closet after that first game or it’s around forever. It works best in groups of people who are at or about the same skill and knowledge level with the game. So if no one in your group has played or heard of it, then go ahead and try it. Don’t read anything online about it. Don’t try to get really good at the game when you aren’t playing it with your group. It’s a game best explored by the people playing it.
Villa Paletti - You’re not going to want to play this all the time, but it’s a good go-to game between rounds of others and it’ll be a novelty for a while. It’s like Jenga, but better and not like jenga at all once you get to playing. Basically, make the tower taller without knocking it over, but there’s a lot more strategy involved. Still, very easy to approach.
Cards Against Humanity is fine as long as everyone has a think skin. It’s just the internet version of apples to apples. It’s sure to be something you can pull out whenever. (Except when your parents are in town). It’ll be replayable and there’s plenty of expansions. It’s a game non-gamers play all the time. So long as you’re cool with how dark and offensive it can get, its fine.
(Each game in this list is a test. It tells you what kind of gamer you are playing with and if you think they’d be willing to dip their toes just a bit further into the pool. Someone who latches onto Dominion might like Race for the Galaxy, Netrunner/Magic, and other games with cards that are more complicated; Ticket to Ride is a good indicator towards strategy games, I might try small world next; People who really like pandemic you can get into other light strategy games, but if they’re not taking to some of your other games, entry-level might be where they stay. Try out something like “The Great Fire of London” and see how they do with a bit of competition. If Dix-It is the most successful and they don’t take to anything else, I’m likely to stay in “party-game” land: balderdash, trivial pursuit being the heaviest I’d go to. Bananagrams can be an indicator of like fast pace think quickly games and so its most deceptive. I would try games like Galaxy Trucker and Space Alert if Bananagrams is a hit and you think they can make the flavor jump, as well as other wordy classics such as Word on the Street or just plain old Scrabble.)
My list currently needs an econ engine gateway game, but the closest to that that I’ve come is Suburbia. Basically you need a litmus test for “classic-euro” that isn’t heavy to get into. This is difficult as a lot of these games can be quite boring if they are simple. I’ve yet to find a good model for it, but Ticket to Ride is the closest thing given it’s “track around the board” set up. It’s still not quite agricola or any of those. A big reason I don’t have a go-to game for this is because economy games aren’t my cup of tea so I have little reason to have them in my library.