Ain't nobody got time for that!
I think this is a different question than asking what the best games are. Sometimes something comes along that might not be the best game, but does things that are unique and interesting that everyone should experience.
Bolded for emphasis. I think this is the most important, and fundamentally fascinating, part of the question. Not necessarily what everyone should play, but what everyone should
experience. And yes, they are two wholly different concepts. When I was in high school, my best friend and I would play FFVIII everyday after school on PC, while my sister would just sit off to the side and watch. At the time, she really had no interest in videogames, but that specific game really caught her attention. Of course, at the time, the cinematics were cutting edge, and that kind of storytelling in games seemed to be fairly unique. I always wondered if the connections she formed with the characters could have been anything similar to the ones we formed with them.
I also watched my friend play through Half-Life on his PC at the time. I always thought it was really cool, but at the time, my only experience with FPSes was Doom and Duke Nukem 3D, which I played entirely with a keyboard, so mouselook really fekked with my mind. When I got my own PC capable of playing it, I borrowed his copy and played through it myself. The experience was entirely different, feeling the tension, the adrenaline.
I dunno what my point is, but to this day, my sister has played through the Uncharted games, the Mass Effect series, pretty much all of the recent Mario and Zelda titles, and has her own 3DS. Even experiencing all the emotions that we get out of gaming second-hand can be enough to entice somebody to expand their gaming horizons. And while some may scoff at the idea of watching other people play videogames, the undeniable popularity of Twitch, and Let's Plays indicates a demand to consume videogames in a non-traditional manner.