What is it about Nintendo's games that makes them good?
I honestly can't be sure. The music is quite often good, and despite their systems being underpowered when compared to the competition, I've never found that the first-party titles for Nintendo systems fail in that regard the way some third-party titles seem to. But those are both cosemetic, so I suppose I should list suspect one here.
Formula. Nintendo's games are formulaic as far as the gameplay is concerned. The difference between playing a handheld Zelda game and playing a console Zelda game are essentially nil when you get down to the nuts and bolts.
You go through dungeons, kill the bosses, gather items that let you beat harder monsters in other dungeons and eventually you save the princess. The differences lie in the way that 3D and 2D Zelda games handle each of those. The 2D Zelda games prefer to use things like block or torch puzzles, and even the boss fights are fairly straight-forward. They are the simpler game but it doesn't mean that they're the easier game.
The 3D Zelda games tend let the player use the aspects that the 2D Zelda games don't have to great effect, the wider range of controls gave rise to the Ocarina, the greater range of movement from an analog stick has given us special sword moves for Link to use. Adding a third axis to the game gave us the hookshot and its variations.
But at the end of the day, Link is still hauling his ass through dungeons, saving the princess. New features might get added, changing into a wolf, putting a scope on your bow, playing music to cause effects, are all just modifiers. You still have to go through that dungeon.
Metroid hasn't changed too much. You're still shooting aliens, running around through alien planets getting keys that happen to be shaped like weapons and armour. I'll be the first to admit I'm a little scan-happy, but handing me an exposition gathering tool is really just another way of getting me to type "examine X". And I always type "examine X".
Mario is still jumping around. He's learned new ways to jump, jumped to new places but at the core of it all, Mario has been and is always a platformer. No matter how many sports games or Mario Parties they make.