During a recent investor Q&A, he answered the question of whether the company might ever sell software on another company's hardware by saying that other hardware just isn't good enough. "Other companies don't share Nintendo's values or traditions when it comes to creating devices," he said. "We are absolutely not thinking of doing that."
He was speaking in the abstract of course (the actual question of the App Store wasn't brought up), but it does seem very clear that Nintendo isn't interested in releasing software on anyone else's platform. Until that changes, that means no Super Mario Bros., no Zelda, and no other Nintendo properties on the iPhone.
Of course, there's no shortage of games on the platform, and if you want quality platformers or arcade-style dungeon crawlers, you've probably already got them. But it's too bad that Nintendo is standing so firm -- if you want to play official Nintendo titles, it'll have to be on the DS, not the iPhone.