I don't know. It's sort of... I guess, variety? I also like their constant innovation and how they keep shaking up how to game. Wonderful 101 is a fantastic example of this. It uses new tech in a great way. It's amazing. But aside from that, you have the variety that Nintendo offers.
Look at it like this. See the Super Smash Brother's roster? Take away the third-party characters, and you are still left with a load of different characters. Despite being kind of varied, pretty much every single one of those characters come from a game that is considered a classic.
Chubby plumber from what is undeniably the greatest platformer series ever, green elf-man from a series that consistently produces amazing adventures. A pair of Monkeys that starred in the most beautiful game on the SNES, a bounty-hunter racer, a muscled beefcake and a wiry prince from the definitive turn-based strategy games, space animals from a space-shooter, and a psychic little boy.
Heck, even the 'generic' Space Marine has an array of creative powers unseen in most other games, has vibrant colors and is a woman.
And every single one of these characters come from an amazing game. The reason that so many people like Nintendo games is that there is pretty much something for everyone. A given Nintendo console will generally have an amazing game in every genre sans FPS shooters. Like, I don't even like Mario that much. I love the crap out of Zelda, Metroid and Fire Emblem, though. They're great. If you compare it to Sony, if you dislike JRPG's then the Vita is a dead system for you. If you dislike PS3 games and the Souls series, the PS4 is a dead system for you.
Add in the fact that they're one of the few people who don't spam the heck out of brown/bloom/chromatic abberation and that they love couch-coop, and you have a very friendly company that offers something for everyone.
Compare that to the western market, where we were so oversaturated in FPS and TPS games that we have to crowdfund anything else ourselves.