Hmm.. I doubt Japan would as they have a well-grounded viewpoint when it comes to nuclear issues. Japan also discovered post WWII that not spending significant sums of cash on defence had some remarkable economical benefits, and they are more likely to negotiate for protection from economic partners (such as the US) than they are to start spending cash on something that they don't really want.

Taiwan wouldn't want to antagonise China by going nuclear. Since the USA is basically the reason that China hasn't reclaimed Taiwan as it's own, I doubt that anyone wants to rock that particular boat...It's an uneasy peace, but peace none-the-less.

South Korea - Probably not, for similar reasons as above. If North Korea attacked them with a Nuke, then US servicemen would also die. Since the US would almost certainly retaliate with some SSBN launched cruise missiles, Seoul doesn't really need to go nuclear for it's own protection. I doubt that the US would be happy with them acquiring Nukes for potential offensive use either - too much risk of escalation. If they went behind the US' back to get them, then the US might just close up shop there, taking the land mines with them. 1 million men would be waiting...

Iran - First chance they get.