The big three in terms of sales would have to be Mario, Zelda and Smash Bros., but Smash Bros. has already done it's dash this generation whereas the other three haven't so when talking about prospective releases it's usually Zelda, Mario and Metroid.

If you go purely by sales, its Pokemon, Mario and Zelda. But if you're going to go into things like 'popularity' and 'Quality', the context gets highly skewed.

The reason Metroid is often put as #3 in the list of Nintendo's 'core titles' is because it was stated by many of the heads of Nintendo to be as such. A 'third pillar' of Nintendo's main three gaming series. If you also go back and look at the origins of the NES, its very creation was to be a game to succeed Mario and Zelda, in both scope and originality.

Any way you slice it, obviously Nintendo has series that do better sales wise (and are more popular). But the reason why Metroid is counted as the 'other other' main title in the Nintendo line-up is probably simply because, like it was designed to be, its the most similar in scope and design to a Zelda and Mario title. And deep down, people know when a new Metroid comes out, its going to be big.  Even if only 1% of those who own the console play it.

I think the reason they are the 'big three' is that they were the three biggest Nintendo made hits starting on the NES and continuing on. Think about it:

NES
-------
Super Mario Bros 3
The Legend of Zelda
Metroid

SNES
-------
Super Mario World
The Legend of Zelda: ALTTP
Super Metroid

Many people consider Super Metroid the best game on the SNES if not of all time.

N64
-----
Mario 64
The Legend of Zelda: OOT

Metroid missing at the N64 point, but by then the legacy of the big three Nintendo franchises have been formed. They are the three Nintendo franchises that many see as defining Nintendo and have a much longer history than any other big ongoing franchise. There is a reason it seems most people pick Mario, Link or Samus when playing SSB.

Mario
Zelda
Metroid

In that order.

I'd actually argue that Kirby has always done better than Metroid on consoles, both in terms of sales and popularity.  But in terms of 'quality' or in terms of being a game near the style and market of Zelda/Mario, Metroid may be the best title to fit that description.

Metroid is usually included for the reason that it was one of the first-party series that got immediate attention with the release of the Game Boy and Super Nintendo, alongside Mario and Zelda. Yes, it goes back that far. Even when the N64 shifted the whole paradigm by having no Metroid and Zelda late, long-time Nintendo fans still considered Metroid to be one of the important Nintendo franchises. The GameCube having a Mario, Zelda, and Metroid all released near one another, combined with the Wii's getting a Zelda, Mario, and Metroid all within the first 2 years of the system's release, seemed to bring back the Game Boy and SNES days in that sense.

Although really, Nintendo's biggest three franchises now are the Mario, Wii, and Pokemon series. Zelda is a comparative lightweight to those, and Metroid hardly even registers as a blip on the sales radar by comparison.

On the Wii...

The Wii franchise

Wii Sports 57M
They're is NO DENYING IT the face of the casual revolution. Plus it's like the one game everybody casual, core, or whatever who owns a wii has played......and liked!

The Mario Kart franchise
Mario Kart Wii 20M
GC MK was at about 6M but these type of sales are insane, plus it's fun is hell

The Smash franchise
SSBB 9M
Yes Mario maybe the face of nintendo, but this is nintendo's most IMPORTANT franchise, why because it has the ability to bring nintendo's new, old, and forgot characters back in the lime lite. In basketball we call it an asst.

I consider MK to be part of the Mario-franchise, Nintendogs is for handhelds (and we're not counting handheld games, according to some people in this thread - that's why I excluded Pokémon), and the Wii series is not core, but casual. No denying that. This thread is about core franchises, check the title!

So, referring to bestselling core games on consoles, I picked Mario, Zelda and Smash. Bros.

Actually, Kirby didn't differentiate itself from Mario as much as Zelda and Metroid did in the early days.  Zelda was a top down exploration, so it was easy to distinguish itself.  Metroid had the "continuous level" concept in both it's early console games, and a different, darker look, so that is how it distinguished itself.  Kirby was a level based platformer.  While it had it's own innovations that made it unique, it is overshadowed by Mario 3 and Super Mario World.

Don't get me wrong, I really like Kirby.  It can't really compare with Super Metroid however.  Also, I am not too sure about the sales and popularity statement of yours.  Do you have numbers to back it up?

Mario
Pokemon
The Legend of Zelda