Snowden highlighted a trivial fact, which is that intelligence agencies will spy. Countries will fight for their self-interest. It's important to remember that countries can do whatever they want if the citizen see that it's in their interest.
Snowden just reminded us to always keep Machiavel in mind. That's how nations operate, and I don't think the UN will change this. It goes for terrorism, oil, climate change, standard of living, electronics, trade. If something is not in the interest of a country, it will probably be dismissed.