I don't think they really aim towards anyone specific, I think they try to make fun feature full games that are accessible, yet have more difficult aspects if you want that. There are a few exceptions though:

Metroid is clearly aimed at the older Nintendo gamer
Zelda is too, even at it's easiest, it's way to hard for a lot of kids.
Fire Emblem is for older Nintendo gamers
F-Zero is aimed at older Nintendo gamers.
I would argue that pikmin is aimed at older gamers

Frankly, I think almost every Nintendo franchise can be enjoyed even more by older gamers than children. Wii sports and other things like that are mostly what kids are able to play.

I don't think anyone misunderstood the question. Nintendo aims at everyone, all ages, both sexes. Their colorful mascots are aimed to be friendly to children but also stay with adults as they age. Their games are gameplay-focused that anyone can enjoy.

Lol, I used to be better at all those games as a Kid than I am now.

Haha not me! I would always get so angry when I played Metroid Prime. 

whole family with a focus on children

Hehe :) When I was a kid it was Super Metroid. Man those were the days. I beat it as a kid but I guess it helped to see my brothers play it too.

People of all ages who don't pretend to be more badass than they are.

games developed by Nintendo were usually made for new kids and OLD kids... you know what i mean...

so basically its for all age...

I'm playing Super Metroid right now, and having trouble! :) 

First off Zelda: OoT and MM helped my son learn to read. Yes it was difficult for him at times, but he'd have friends over and eventually they'd figure it all out. Which is a part of the game play that's sadly lacking in today's world.

Nintendo games are always focused on family fun. Sometimes they gear a little younger (Epic Yarn) or a little older (Twilight Princess) or more female (Wii Fit) but in all cases anyone can play any game (but not every game appeals to everyone). Which is why parents always feel comfortable buying Nintendo systems/games but also why a lot of gamers don't like Nintendo, because they want to be catered to specifically to their age, likes, skillsets.