Well it is hard to explain but i will try my best. Its really the sum of all parts of their games, its the way everything in thier games come together to make it timelessly enjoyable from the controls to the artstyle to the music and sound effects everything just fits perfectly together to make an enjoyable game.

For eg for those whoever played SMW on snes when you play the first level and you hit all the turtles on the platform the whole effect of the catchy music the sound effect when each koopa is hit and the extra life sound effect everything just fits together neatly into an enjoyable single moment, basically it just feels good to do. That is nintendo magic everything in their games they try to make it enjoyable to do, because really that is the basis of video games enjoying what you are doing on screen.

In mario 64 the speed the camera moves behind coupled with the timing of his animation makes it enjoyable to just run around and jump. Only now that western games have become more prevalent that i realized all these were not by accident, for eg when i first played gears of war i thought nothing could stop me from enjoying it, it was a 3rd person shooter had local co-op play through the campaign and had possibly the best graphics at the time this game is perfect, only to my horror that somehow everytime i shot someone they died of a heart attack why did they die of a heart attack, then i realized they just did not know how to make it feel satisfying, imagine playing a shooting game that doesn't feel satisfying to shoot people thats my example of a completely terrible game.
I can still play starfox 64 to this day and still enjoy because its a shooter that feels satisfying to shoot something no matter how many times i do it, that is nintendo magic.

Pulling out a piranha plant out of a green pipe

Sucks some dissed it for its "kiddy" art style.

I really like platformers. My best memories and current experiences on platformers are on Nintendo. My favorite game series is a platformer and it's on Nintendo. That's all I got.

Consistency in putting out quality games.

Extreme levels of creative and mechanical polish combined with a lighthearted fantasy aesthetic.

I know, that's why I started both sentences with "most".

It's not like other companies don't have the magic, the chances that you play their games are just smaller.

Crash bandicoot and Abe are nostalgiac for me. They could fuel the tank on nostalgia alone. Abe New N Tasy will be soon out on the Wii U. Crash, alas, has disappeared, possibly forever.

I don't buy the nostalgia claim at all. I never played an F-Zero game (GX) until I was an adult. I didn't play Metroid Prime or Super Metroid until this year and those are my first metroid games. Super Mario Galaxy was the first 3D Mario I ever truly played. Mario Kart Wii was the first Mario Kart I ever truly played a lot of. Brawl was the first Smash game I ever truly played a lot of.

I still felt the "Nintendo magic" with all these games despite having absolutely no nostalgic links to them. Even Nintendo games that I feel are over rated like Ocarina of Time, have that magic. I even feel silly using the word magic, but there isn't any other word to describe it. I can explain to you why Super Smash Bros. is such a technically superb party brawler, but I can't explain to you why it's so fun to play a game that literally makes me hate my friends. I can explain to you why Wind Waker is one of the most well designed games of all time, but I couldn't tell you why a cynic like me cracks a smile when Link gets the Master Sword and realizes for just a second how much of a bad ass he's become before becoming humbled in it's presence. I can explain to you all the smart design choices that makes back tracking in Super Metroid fun, but I couldn't explain to you why feeling lonely in Super Metroid is fun. And I couldn't tell you why all the unexplainable feelings I get from these three completely different games is, in truth, the same single feeling.

Nintendo makes games that make people feel something that can't and need not be described, because everyone feels the same thing. It's like Nintendo crafted a secret language of pure emotion that only it's players can hear, speek, and understand. That's magic.

Same goes for me, I love the Bandicoot games from Naughty Dog, it is that one franchise from my childhood that I will always look back at (and always hope for a new game that makes me relive my childhood). Spyro and Abe are also somewhere up there. The way Spyro and Crash got thrown around like an old puppy after the PS1 era just broke my heart.

I wish they would both get the same treatment that Abe got with New 'n Tasty. That game stays true to its roots, a gift to all the old fans.