In terms of sales it's:

2-D Mario
Pokemon
Wii

but in terms of critical acclaim it's:

3-D Mario
Zelda
Metroid

2-D Mario
Pokemon
Wii

Under the reasonable definition of Core, but then based on sales, it would have to be Mario, Zelda, Kirby. In terms of internet hype, yeah it's Mario, Zelda, and Metroid.

Whenever anyone mentions the big 3 for Nintendo its always Mario, Zelda, and Metroid. However, you can argue that DK is just as big if not bigger than Metroid.

Personally Metroid >>>>>>>>>>>>>>>>>>>>>>>>> DK or any other IP besides Mario/Zelda.

Zelda, Metroid and Star Fox in my opinion. Mario is too casual friendly to be there, same for Kirby, and I love DK but he's been missing for so long...

metroid is there because of critical acclaim. saying that, pikmin recieved aqs much praise as prime 3. But it is these 3 characters which are seen as the traditional holy trinity

1° Zelda
2° Mario 2D or 3D
3° Metroid

I will bet against anyone that if DK was resurrected, the holy trinity will no longer have Metroid as one of its members.

zelda
mario
pikmin

I always consider Donkey Kong a part of the same IP as Mario, and of course he hasn't had a big game in a while. Smash Bros. is bigger too, but it's sort of a mix of IP's...

Animal Crossing is 'core' in one sense of the word, but I don't think it is in the sense we're thinking of.

Metroid is not that big an IP really, but it's one of the more development intensive series on Nintendo consoles these days, that's why I consider it a 'big game', the costs to make it rather than just the sales it receives.