Nearly all of Nintendo's titles live up to what they're trying to be, and you can rely on getting a quality experience when the game comes out.

My favorite things have to be the polished gameplay and the charming atmosphere!

Polish and high quality gameplay

So much about them is great, but in particular the gameplay experiences. A good example of what makes them better is comparing Zelda and Fable. I love both games. recent Fables have been prettier than recent Zeldas. But the Zelda games have much better structure, pacing, depth and gameplay variety. Each Zelda item is usually unique and not just an upgrade of what you had before. It does things in the world and not just as a new method to attack the enemy. Each zone is thought out and not just scenery for the journey.

I used to be a brother...

Pikmin 2 used to be my favorite game of all time but not anymore...

Pikmin remains one of the best IP's ever though.

The commitment to design. Some may see it as a fault, but Nintendo seems to approach projects from game perspective first and everything else second. Playing a Nintendo game is like going back to 16 bit era when story and voice acting and cinematic feel were not possible, just with updated visuals. To me Zelda is pure gaming, exploring, fighting, puzzle solving and discovering secrets.

It is a big reason why I buy every system they make eventually, it strikes a contrast with much of modern gaming.

They are fun to play.

Local multiplayer, pretty much the only developer left that pays much attention to it.

There are plenty of reasons, here's one of them:
Look at how link looks at the player and others in Zelda Skyward Sword (example) and look at how characters in something like TWD look at others (example), you'd notice the animation and eye movement is a LOT more accurate in Zelda, so superb animation and quality.

I'm having difficulty explaining why I like Nintendo. I guess every time they announce a new game, I get excited to see what it is. For me, Nintendo offers very nice looking gameplay.