I'm not sure I have anything fresh to add to discussions of the sudoku craze. Rob Walker, I think, had a column about it in The New York Times Magazine a while ago, and these ideas are likely derived from that: Its universal appeal probably stems first and foremost from the media feedback loop that has been created about it, affirming it as some aspect of the zeitgeist one should be aware of and assuring everyone that it really is fun and addictive and so on. Beyond that, it transcends language barriers; it liberates users from needing to have verbal skills (like punning, thinking of secondary definitions, etc.) or have a wide base of learning (no trivia or familiarity with history, culture, entertainment, or the past in general is necessary); and it can be made by machine at various levels of difficulty and is thus endlessly reproducible for a wide spread of people, regardless of skill.
The purity of the logic to solving the puzzle has its appeal -- no tricks or guesswork, just sheer deduction. There are no layers of meaning to it; just a pure discharge of mental energy in something elegantly useless. It's the kind of intellect our culture celebrates -- the useless noncritical kind -- and it epitomizes how Americans often view smart people, as having the ability to perform pointless tasks with expediency, as having this cranial power that is not directed toward anything relevent to anything else. Other cultures seem to have public intellectuals, and a concept of such a person as engaged with social reality, analyzing culture and politics. (America has vapid pundits whose primary function is to "entertain" rather than instruct, staging an ideological stalemate to convey the sense that having an ideological perspective is either pointless or as basically irrelevent as rooting for a sports team. You won't find a single moment of intelligent discourse on commercial TV in America. Maybe this is true everywhere.) Sudoku is a good way to render intellect harmless. (So it's fitting that it's being rolled out for that other brain-zapping device, the cell phone, according to a trendpiece -- that prompted my own trendpiece -- in yesterday's Wall Street Journal.) That alone may account psychologically for its addictive qualities -- it's enjoyable to burn mental energy and the restlessness that comes with it, the feeling that one should be doing something productive. By producing the right numbers in the right places we can control and master that need to produce without confronting any of the difficulties that come from making something useful or social.
The WSJ article concludes with a quote from a woman who is trying to control her habit around her boyfriend, so that she can "pay more attention to him." Sudoku not only dissipates intellectual energy, but it also exhausts our need to focus -- it forces one to concentrate intensely on something private and hermetically sealed off from reality, and then you can return to reality afterward with the attention deficit that's expected of all of us to function in our media-oversaturated lives.