Nobody wants to read Great Expectations, but in high school we were forced to. Nobody wants to read Shakespeare, but in the interest of having more cultural knowledge, all (or most) of us have.
Reading, watching, or gaming outside your comfort zone is a way both to discover more about yourself as a person and your own interests, and also about what is widely regarded as "good." Blade Runner isn't everyone's cup of tea, but anyone with an interest in film should see it. I'd rather drop fifty pounds on my crotch than read Pride and Prejudice again, but I have (and you probably have had to read something from that time period, too.)
Now, video games have been around for long enough that there are games considered to be classics, and there are games that are credited for inventing, reinventing, or epitomizing a genre. Hundreds of games come out yearly and with dozens of available outlets, game reviews can be accessed with unbelievable ease.
"Gaming outside your comfort zone, redux" is my schpiel on why you should play games you don't think you'll like. Limbo is an awkward, dark, linear platformer/puzzler with a specific aesthetic that won't appeal to most. Grabbed it for fun during a Steam sale and didn't regret it one bit. Like Mass Effect? Try a more action-oriented role-playing game, like Fable or Kingdoms of Amalur: Reckoning. Like the Grand Theft Auto games? Try another open-world game in a different setting: more serious, higher-fantasy games like Fallout and the Elder Scrolls games come to mind.
I'd never thought I'd like StarCraft as until I bought it I only had a passing interest in games like Civilization . I barely even liked Tower Defense-style games. But as it turned out, the micromanaging I was so fond of in RPGs translated into unit control and attack timings.
Like Halo? Try Borderlands for something a little less linear. Like turn-based role playing games? Try something like Final Fantasy Tactics or Star Ocean games for a slightly different take. Play Oddworld: Stranger's Wrath and shoot bees at people.
Play WarCraft and see what all the hype was about. Go back and see God of War's female counterpart tear shit up in Heavenly Sword. Experience the PlayStation's "Halo Killers," Killzone and Resistance: Fall of Man.
Like relatively casual games with a high skill cap, good aesthetics but are easy to pick up and fairly short (e.g. Portal)? Try Bastion or Odin Sphere. Are you a masochist and like brutally difficult and unforgiving games? Try Demon's Souls, Dark Souls, Mount & Blade, War of the Roses, or Ghosts'n'Goblins.
Don't be afraid to try a cheap, older game that some consider to be the epitome of gaming. Final Fantasy VII is still a pretty good game, as is Final Fantasy X. Some of the storytelling in these games, as well as in the N64 and SNES Legend of Zelda is second to none. Like rhythm games? Get RezHD on XBLA for a surreal music-game experience.
Pick up an old Pokemon game (Snap or Red, for example) and see what everyone was talking about ten years ago. Nazi Zombies is only so much fun - Left 4 Dead, Resident Evil (especially RE4) and Dead Island provide variations on the co-operative zombie smashing experience. L4D and Dead Island are more of a scavenge and survive with friends while RE games tend to be fairly linear, one against many type shooters.
Play weird games. Play Katamari. Play story-driven games like Dear Esther. Try dungeon crawlers, from Diablo to Dungeons of Dredmor. Get Heroes of Might and Magic or Dungeon Defenders and fight with friends. Try something from every genre, and something weird from every genre you don't like - maybe Burnout is your racing game when Forza rubbed you the wrong way. Maybe saving the princess doesn't tickle your fancy as much as getting scared shitless in Amnesia does. Bored of shooting terrorists? Kill some twenty-foot-tall trolls. Get out there and game.
Here is a list of games that "defined" retro gaming consoles: http://www.racketboy.com/guide/games-that-defined-retro-gaming-machines
"hidden gems" from past generations: http://www.racketboy.com/guide/hidden-gems