I just broke one of my strings on my Ibanez and was wondering if I don't restring it, like right after it breaks if the change in tension with hurt the neck? Because I don't really have the time today to go get some strings. Would it be bad to take all the strings off and leave it that way untill I restring it?
It'd be worse for the neck if you take all the strings off entirely, because the neck is used to having tension on it. One string isn't going to cause a noticeable change in the overall tension on the neck, so there's nothing to worry about. Still, if you're only talking about a day or two, it's no problem either way.
Even if you left all of the strings off for a while and the neck bows in either direction you can adjust it with the truss rod.
Jackson SLSMG Ibanez Jem7v Jackson SL3

Line 6 Spider Valve 212

Ibanez Weeping Demon Wah