Murray Rothbard thought that the first users should be the owners. http://www.lewrockwell.com/rothbard/rothbard157.html So under his scheme, the downstream owners would have to buy the river from the upstream owners to prevent them from polluting.
I think that there's something wrong with an upstream owner polluting the river and causing damage to people downstream. The situation is analogous to burning poisonous chemicals on land and letting the wind currents carry the chemicals onto neighboring property. In this case the burner would be liable.
The overall point is that pollution can and should be handled as a property-rights matter and that the state need not and should not "regulate" pollution.
I am curious. How do you go about deciding ownership on a long river? What rights does "owning" a river give you?