Well, when I was eight I basically flipped a coin and asked my parents for SNES over Genesis, so I was very much platform agnostic at that point. My favorite games on SNES were Super Mario World, F-Zero, and Super Street Fighter II: SMW because of the interesting levels and secrets; F-Zero because of the music and sense of speed; and Super Street Fighter II because of the special moves and, despite losing every time, playing against my older brother. 

When I was 13 I received an N64 for Christmas. Super Mario 64 mesmerized me with its 3D graphics and huge open-ended levels; Shadows of the Empire captivated me with its Star Wars license and atmosphere; and Turok captured my attention for its guns, its dinosaurs, and, let's face it, its violence.

Only later in life, with hundreds of games under my belt and with a more nuanced understanding of game design, did I begin to fully understand everything Nintendo did and does right. Looking back, that decision to pick SNES in 1991 was probably the smartest gaming decision I've ever made. 

This... 

...and this. I would use the same words as the OP to describe some epic moments in games I played in my childhood...and since I didn't play Nintendo games as a kid, I now fail to understand "Nintendo Magic", even though I really try.

Hmm, think it varies. 

For some it means convention, for others it means rehash, nostalgia, fun, etc. 

For me it's a little of everything. It's safe, comfortable, predictable, fun, nostalgic, etc. 

It's that alien substance used to make Zelda games.

Despite not growing up with Nintendo, I have felt the "magic" in numerous games this past year. Namely Wind Waker HD, which is perhaps the most magical gaming experience I've ever had. It was truly unlike anything I'd ever played before. Nintendo just knows how to make charming experiences that stay with you.

(Although this isn't a quality exclusive to Nintendo.)

This is fairly close to what I'd say, although I think Nintendo's appeal is also a little quirkier, where my experience of Disney films is usually that they aim for something more designed to suit the masses. Something like Pikmin has a very unique charm but it's not the same kind of people-pleasing charm I see in Disney films.

I'd describe it as a Japanese combination of charm, innocence and eccentricity. I've seen a few non-Nintendo games try to capture the same kind of charm with varying degrees of success. I loved Viva Pinata, for instance, but the voice acting in that felt like it pandered a little too much to children, which Nintendo games generally don't do. I think LittleBigPlanet aims for a similar kind of charm but does so less successfully; the production values almost feel a little too Hollywoodised, if that makes sense. It's cute but feels somehow soulless.

Then again, Nintendo don't always nail that charm, either. I wasn't a big fan of Super Mario Galaxy 2 because it just felt like it was trying too hard to imitate the magic of the first Mario Galaxy game.

Well, not quite the same imo. People don't say Mario Kart magic, or SSBros magic, they say Nintendo magic, not refering only to the one game like the example you said. It's the same when people say Naugthy God instead of Naughty Dog, because gamers know some companies, more often than not, do deliver quality games.

Nintendo Magic = Getting your wife to sit down for hours and play video games with you.

Nintendo Magic = Allowing me to play games not suitable for kids(on a home console)while my kid watches TV in the same room, yet she can't see what I am playing

Nintendo Magic =  Playing Mario Kart with my granny and child and actually having both of them enjoy themselves.

Nintendo Magic :) Shall I continue?

Most of the Nintendo magic comes from nostalgia. Most of us grew up with Nintendo, because they had the most popular consoles and each of them had ground breaking titles.

Also, most magic moments have fantastic music combined with it that sets you in the right mood. Music is such a strong medium, it does help to make you still appreciate old games.


- Intro of OoT is a classic example.
- same goes for final Bowser in Mario 64. If some organ starts to play in the background of a 90s game (same for OoT Ganondorf), you know sh!t's about to get serious. Also the color scheme of Bowser is just phenomenal there

About the Twilight Princess reveal trailer, I tend to use this video because the crowd goes nuts!
https://www.youtube.com/watch?v=VE2Dc1sx71U
At first I get goosebumps, later I even get teary-eyed and smile uncontrollably. Every time!
The way this trailer slowly reveals what franchise this trailer is about combined with the incredible Conan the Barbarian music playing in the background is just so much joy at once. Especially in a time where 3D videogames started to actually look good and people desperately wanted a realistic looking Zelda 3D game.
To me this is the best game reveal of all time, it created so much hype to me like no other reveal could ever do. Sadly I was not blown away by the game itself, I am more of a Wind Waker guy, but that's another story.

For some but not all. I for one avoided Nintendo as a kid and now love their games and consoles.