It depends on how you use it, but at least a couple of acres. Potatoes are quite efficient, and rabbits and chickens can pretty much live off left-overs and patches of land that are otherwise unused. That would be a rather boring existence, though.

3-4 acres should be more than enough for the basics for a _small_ family, if you accept to buy the more exotic items from a store, and that you will probably never grow fat.