"Property is theft" is not an anrachist saying, but a communist one that anarchists have appropriated.
Nice to hear the Zapatista idea mentioned, as it's a very interesting model. It is not an anrachist system, of course, because the people do function as a government. It's just a local government system in which everyone has a very direct influence on the decision-making process.
Of course, such a system has it's drawbacks too. What One which has already been raised above is -"What happens when a consensus cannot be reached?" Failure to reach a consensus on a difficult or divisive issue, in particular, can divide a community. Indeed in such a 'bottom-up' system, disagreements within the community over political issues can cause serious clashes - when you are actually directly involved in making the decision, rather than having it made for you at arm's length by your elected representative, you can come to invest so much emotional capital in your side of the argument, that you develop ill feeling towards opponents of your position. (I hope that last bit makes sense.)
Nonetheless, whether it would succeed in all settings, the Zapatistas' model is very interesting.