Two main features about Nintendo come to mind that define it.
The first is polish. More so than any other dev I can think of, they polish, and polish, and polish some more. Like a master craftsman, they seem to try and make sure that whatever they are making is the best example of whatever that is they can come up with.
So, they have been getting sloppier over time. Newer games have more rough edges relative to their total content than older ones do, but even so, they are still quite obsessive over getting every little detail 'just right'
The other point they have going for them is innovation. This is most frequently argued about, and often misunderstood. Because people see yet another mario game, and conclude Nintendo never tries to do anything new.
The problem is, Nintendo's form of innovation is gameplay innovation. Not narrative or character changes, but changes in core mechanics and gameplay concepts.
Nintendo in essence invented the platformer. (Not quite, but to a large extent every platformer in existence after then owes something to donkey kong and mario)
They also basically invented a lot of basic stuff about 3rd person 3d games. Mario 64 defined the way most games ever since handle 3d platforming, basic aspects of character movement, camera controls and so on, that you see all over the place.
Zelda after it more or less invented the idea of locking on to something in the environment...
They do it with hardware too. Not always to people's liking, but you can see it nonetheless.
While analog control was around much longer, Nintendo made the analog stick a thing.
Imagine your game controller without analog sticks.
Because that's probably where you'd be right now without Nintendo's hardware innovation.
For that matter, add to the list the dpad, and honestly, the standard 'modern' controller design everyone now uses.
The Playstation and Xbox controllers are ultimately evolutions of the SNES controller layout.
Handheld gaming... That was Nintendo too. You might wonder, because there were others that have tried it too. But Nintendo's first attempts at handheld gaming were the 'game and watch' things in the early 80's...
The wii... Yes. Not to everyone's tastes, but certainly nobody else would seem willing to try and build a console around motion controls...
When berating Nintendo for being 'weird' and 'different', remember that we owe a lot of stuff we take for granted in modern gaming explictly to Nintendo. They invented it, everyone else copied it.
Just because some of their ideas are bad ones, it's worth remembering just how much basic stuff we take for granted in games can trace it's origin back to something Nintendo did.
That doesn't mean of course you have to like what they do. It may not be to your tastes. And honestly, while I said all that, I'm not sure if modern Nintendo can still pull off anything so significant that it'll permanently alter the entirety of gaming. (again) like so many of their controller innovations have in the past...
Nor can I really imagine them creating entirely new genres of games as they have in the past...
It seems unlikely. Then again, the thing about those innovations is you don't see them coming. So who knows.
Many will seem like gimmicks, some could change things so dramatically you'll wonder what we did without them.
It does seem unlikely though.
I guess the overall point is, Nintendo takes risks with game mechanics and hardware design that it seems other companies of similar size wouldn't attempt.
Can you imagine anyone else trying to build a Wii? Or the Wii U after it? Which is weak compared to it's competition but has a strange input device?
Whether that was a good idea or not, those are pretty risky moves to make when the name of the game in the console business has been 'have better hardware and better games than your competiton' for as long as anyone remembers it...