I don’t normally meme, but this one caught my attention. I normally GM, so my focus is there.
1) Dungeons and Dragons: some flavor of this, though my inclinations are for 3E or the Basic Set for opposite ends of complexity. It’s the grandfather of gaming and should be experienced if only for that reason, but it’s also capable of delivering some cracking good games along with BF Skinner-influenced character growth that can be a game all its own.
2) Villains and Vigilantes: because everyone needs a chance to play themselves with super powers, and everyone needs to see that characters can have different power levels (an aspect of the random power generation charts) while still contributing equally to play.
3) James Bond 007: because the default structure of one player with a highly skilled PC rather than a party will show you why you don’t need parties, and therefore highlight why you do. Plus, the system is a great example of how focusing just as much time and effort on things that matter to a Bond story (car chases, seducing people, gambling) as it does on combat keeps combat from becoming as dominant as it is in other systems.
4) Pendragon: because, like James Bond, it is a wonderful emulation of the source material, it is a combat game where the combat is fast and simple, and because the rules for personality traits show you where surrendering your character to the dice can be a good thing.
5) Amber Diceless Roleplaying: because as a GM Amber really forces you to think about challenges, character power levels, inter-party rivalry, sharing authorial control, spotlight time and parallel plotting without having any external crutch (read, dice) to fall back on for your decisions. This one should be later in the list, because running Amber is a masters’ course in GMing.
6) Call of Cthulhu: because you need to have the heroic paradigm inverted, playing in a world where the spoils of victory are alienation and madness but that the fight has to be fought anyway. And because it will teach you how to plot an investigative mystery, which is very useful in almost any other game.
7) Paranoia: because sometimes all the normal rules of play – that you have a chance of winning, that the world is fair, that the party is working together – need to get tossed out the window and followed with an array of blaster fire. And because there is just nothing else like it out there.
8) Buffy the Vampire Slayer RPG: because there is no better system for a powerful titular hero with a circle of assistants; because it is a spot on emulation of the source material that is translatable to much other pulp and heroic fiction, because it builds on the lessons taught in V&V about not mixing power with effectiveness by showing you how to use those for story arcs and character growth.
9) Star Trek (Decipher edition): because it remembers that serial fiction is as much a vehicle for drama as it is action stories, because it teach you how to build such tightly constructed stories in ways that still don’t railroad your players and because it has a kicking cool space combat system that keeps every player involved (even if the person to person combat system needs real work).
10) Feng Shui: because sometimes you just need to kick ass, with no western style genre guarantees that you won’t die in the process. And because it has solid guidelines action movie game construction, moving the PCs from set piece fight to set piece fight while making the whole greater than the sum of its parts.
11) Any PBEM: I’ll echo mylescororan here – because you need to learn that there are other valid media for gaming, with their own quirks and charms
12) Any LARP: again, because you need to experience another style of play, at least once.
At least, that's my opinion