Countries will stop trading on centralized exchanges which will cause the price to temporarily drop. But since the network is decentralized, as long as there are still desire for the currency and someone willing to accept it, the cryptocurrency will always have value.
That being said, Bitcoin and Ethereum are reaching the point where they are starting to have a legitimate impact on the economy and it is probably in their best interests not to ban, but to legalize and regulate the currency (like Japan and South Korea are doing).
I'm hoping countries will follow South Korea and Japan, and not China and Russia. It makes sense for countries with a high risk of flight of capital to ban, or at least severely regulate, exchanges. For those with less risk, it makes sense to regulate them only mildly.