Hmm...while I have no doubt that most if not all mentioned games are good (if not great), I'm mostly left wondering why they are must plays. Why would you recommend said games? I may be wrong, but I feel lots would just answer "because I like them". And that isn't exactly a good strategy (I mean...I just watched suicide squad, but I wouldn't list it in a list of 'must watch' movies). It's mostly a list of games I would recommend to people like my girlfriend (who is pretty "meh" on games to begin with).
I thought up some good games, compared them and scrapped a bunch. Even now, the list is longer than I want to. The reason is that each game has some sort of 'niche' to it. A "why does this game needs to be played?" that, in a way, enhances the lives of the participants.
Oh, and...I do take the liberty to list a few non-video games.
-Chess (board): no, you shouldn't become a grandmaster, but you really should at least have played enough rounds to know how the pieces move and interact. There's a good reason this game is played for centuries.
-Carcassonne (board): a city building game that's quick to set up and put away, can be grasped by anyone quickly, has more depth than it first appears and is one of the best ways to prove to players that board games can be more fun than monopoly (runners-up: ticket to ride, splendor)
-Pandemic (board): while rather complex, it's still the best co-op game on the market. It's tense, it requires teamwork and deliberation, and since you're not adversaries you can always help out everyone.
-magic: the gathering (Collectible Card Game): this is a tricky one to learn, because introducing someone to all the rules at once just goes over their heads. But the open-ended nature of the game, the way you have to make your own deck and anything that can interact with anything is great in its own right.
-Plants vs zombies (mobile
/PC): its this sort of game that tablets were made for. And not only does this introduce well to people who normally don't play games (you instantly grasp the concept), it's also still one of the best tower defense games to this day (though I may be missing some gems on this one).
-Simon Tatham's puzzle collection (mobile
/PC): this is a collection of logical puzzles. Not only is it free, feature proof and quick to pick up and play, it has plenty of difficulty levels and can be played instantly (runners-up: solsuite, puzzlerame)
-mini metro (mobile/PC): this game is so simple yet deep I barely know how to describe this one: symbol-shaped metro stations pop up on a map, and you need to transport people (smaller icons next to the station) to their destination by providing metro lines. It's so simple and elegant that you can start playing it in seconds. But as the number of stations increase, you really need to start planning your lines and trains for efficiency. One of the most elegant yet deep games on the app store.
-cook, serve, delicious (PC
/mobile): while part restaurant simulator, the core of the game is a stress simulator and typing lesson (at least on PC). You basically attempt to push back the chaos while serving as many customers as fast as you can without making mistakes. Both in theme and execution, this game is pretty unique.
-Mario vs Donkey kong (GBA): when it comes to puzzle platformers, I just can't think of a better one: it's both casual and fun, quick to pick up and grasp, and has all the details you come to expect from a nintendo title (runners-up: Abe's Oddyssey, Abe's Exoddus).
-Zelda: a link to the past (SNES). While the "which Zelda" is a debate entirely, they provide a good combination of puzzles, combat and exploration. I even had a friend who played this with her boyfriend: he would do the fighting, she would do all the puzzles. while the 3D Zelda's are great in their own right, I can see how the isometric perspective has some advantages over it.
(runners-up: link's awakening, oracle of seasons, oracle of ages)
-lost vikings (SNES): I looked, but this exercise in proper teamwork is still without a true spiritual successor. The thing about this game is that you have to properly use each character's strong points to properly traverse the levels. (runner-up: lost vikings 2)
-wii sports resort (wii): assuming you've got enough wiimote +'es, I would consider this the best party game ever. None of that cartoony Mario characters or stupid minigames, but pretty neutral sports and interesting ideas that will always be unique to this console (runners-up: wii sports).
-kirby: epic yarn (wii): while I'm not much of a fan myself, this is probably the best entry point for non-gamers: a platformer with perfect co-op, where you cannot die and where the theme is one that doesn't turn off women (my girlfriend won't play King of Tokyo with me because she doesn't like the Godzilla-theme, so it's not like that stuff doesn't matter).
-Don't starve (PC): roguelikes aren't for everyone, so I'm hesitant to give one a spot. But if one has to have a spot, don't starve should have it. the premise is so simple: don't starve. So...go out, grab some stuff, craft some more stuff and die sooner or later because you really need to plan ahead more than you're currently doing.
-Doom...the original version (PC): of course there were plenty of great FPS'es after doom, but strangely enough, hardly anyone has stood the test of time so well. I mean...aside the resolution, the game still plays great. It's also so simple: shoot enemies, avoid incoming fire. Nonetheless, it was never boring or repetitive.
-red alert 2 (PC): when it comes to RTS'es, things pretty much HAD to become more complex at some point. If you ask me, red alert 2 (and Yuri's revenge) was that turning point: it was the last game where units had 'just' one ability you'd activate by doubleclicking on it. And starcraft had always the whole thing where plenty of micro and abilities where what determined the winner. RA2 was IMHO the last one where you could just harvest some stuff, build an army and just moved out when you felt you were strong enough. It doesn't make other RTS'es in any way bad, but their entry level just isn't the same (runners-up: starcraft, starcraft 2)
-Burnout paradise (PC): it wasn't until a broadcast from errant signal why I understood what it was about burnout paradise that I liked it so much over later racing games: those recent need for speed's are more about shiny cars than about the act of racing. burnout paradise is more a spectacle than a race, but it's great at doing that. It isn't so much of having the fastest vehicle but the act of knocking each other off the road. It's as if you're playing dodgems on a road rather than just attempting to maximizing your speed in order to shave a couple milliseconds of a record lap time.
-the sims 2 (PC): a hard choice, as I barely played this one. But I recognize the appeal: there's something enticing to building, whether it's a city, a spaceship or a dreamhouse and equally dreamy 'perfect' relationships (runner-ups: the other sims games...and I guess anno and sim city clones as well)
-Tetris (everything and the kitchen sink): you can't NOT have tetris on a list like this.
-The walking dead, season 1 (PC): a classic example of how games shouldn't all be about fun to be great, where choices matter and emotions shine. I've made a case for this one to non-gamers...even if one of 'em picked this one up it would be worth it.
-antichamber (PC): simply put: the best 3D puzzler ever. Smart puzzles that requires all sorts of thinking, an abstract theme, interesting and differing mechanics and it proves perhaps more than anything else that games can be art. (runner-up: portal)
and last but in no way least:
-rocksmith 2014 remastered: there's just no way around it...all the guitar heroes and rhythm games were meant to at one point end up with this: a valid and fun way to actually learn guitar (as in: an actual guitar...not a lookalike). Other games I've recommended to people who don't play games...this one I recommend to those who barely know what a computer can do. If you're in any way interested in a guitar, this one is more of an asset than most other accessories. It's just...that good.