We're moving from a period of limited public information to one of so much it will be primarily processed by computers. People worry about privacy rights: how do we limit the spread of knowledge about us? I speculate that in the near future publicy rights will be more of a concern: how do we keep others from limiting this spread?
(Making information public about me almost always makes some information public about others as well. So the rights to publicy and privacy are in partial opposition.)
Dictators have shut down the internet in their countries several times over the course of the Arab Spring, trying to keep protesters from organizing and the rest of the world from hearing about it. China heavily limits the spread of information they find threatening. People recording police is a growing check on their power, from the Rodney King beatings to the recent pepper spraying of passively resisting protesters, and while the police have been trying to limit this, the courts have recognized that this is (and needs to be) legal. As it becomes cheaper and easier to log everything, the main force opposing publicy will be authorities abusing power.
When information is limited and one-sided, we need privacy rights to protect us from surveillance. When it is abundant and many-sided, we need publicy rights to protect our sousveillance.