Okay, let me get more specific. Have you ever played Shadow of the Colossus?
There's a game with very little story, yet for some reason it had a GREAT untold story. There is so much you are thinking must have happened in that realm, yet little of the story is told. And like Mario, it doesn't need a story because you're going from Colossus to Colossus. However, like Sal gave in his example, in Journey (which I have yet to play), there is a great untold story, told with the dynamics of the characters, with the environmental objects and worlds you cross, told by the swaying music. It doesn't even need a story that the game conveys an emotion. (@Xxain, read that it'll answer your story whore question).
The last paragraph is one that troubles me the most and I'll tell you why. Mario is a character that represents the company as a whole. It's the icon of the company, and close enough to being the icon of the industry. Should a character with such a great reflection convey vaccuity? Or should he convey emotion? I believe emotion.
When Super Mario offers themes that are limited to children, it alienates the folks who are older who would also like to enjoy it. As such, many in this thread say it is the example of a game that is not age restrictive, but it is the exact opposite, it restricts to kids. On the flipside, nothing in Disney movies makes me, as an adult, and as a child in the past, want to shut it off. Rather, I want to stay and watch it.
That's the all-encompassing quality a Mario game should have, as the icon of Nintendo. Anything else would be selling it short, to make a pun. ;)
I'd disagree about Shadow of the Colossus. Shadow of the Colossus IS a story driven game. While the story of Shadow is told in a very minimalistic fashion I feel that it is still front and center. If it wasn't for the story, Shadow of the Colossus would have been a really mediocre experience.
The key thing is this. Team Ico decided to tell a story in a unique and creative way. Mario games are not really trying to tell a story at all.
If you want to talk Disney, let's talk Mickey Mouse. When Mickey started out he was a very mischievious character, and at times a bit of a pain in the ass. As time went on, his rough edges were smoothed out. He became friendly, cheerful, and helpful to a fault. In general, corporate mascots are cheerful and bland faces that are designed to appeal to as broad of an audience as possible. Your representative is generally the least objectionable person you could find. And that's why Mario represents Nintendo.
In addition, I think story would be intrusive in a Mario game. When I'm playing a Mario game, I simply want to pop it in and play. Honestly, if I had to sit through more than five lines of dialogue, I'd get fidgety. There are other games I play for story, but that's not what I'm looking for out of Mario.
But, why exactly is it that you feel modern Mario games are so kiddy? I've been replaying Super Mario Bros 3 lately, I've played quite a bit of NSMB, and I've been playing Super Mario 3D Land regularly since its release. I just don't see what makes Super Mario Bros 3 any more or less kid-like aside from the retro visuals, which are simply a product of its times.