Can governments ban bitcoin?

Though it's possible for laws to be passed which prohibit the ownership or use of cryptocurrency, there is no way to shut down the bitcoin network or prevent people from using it directly. 

Because of the distributed, open-source nature of the bitcoin network, there is no central "kill switch" that be triggered by a government trying to ban bitcoin. There is no central bitcoin organization that could receive any type of lawful "cease and desist" order. The network is run by people all around the world.

Even if a single country were successful in shutting down bitcoin within their borders, bitcoin would continue to operate as usual outside of that jurisdiction.