Because of course, spying on people outside one's own country is what intelligence agencies are supposed to do.
This isn't true.
"Richard O'Dwyer, a computing student at Sheffield Hallam University, faces a potential 10-year term in a US jail despite never having been to America or using web servers based in the country."
http://www.theguardian.com/law/2012/jan/13/piracy-student-lo...
Throughout the history of America we've seen the tension shift to one side of this rope or the other. through a series of Supreme Court decisions in the very early 1900's (during the Spanish American war) it was settled at the highest level that American occupied territories do not have a right to self-determination nor to many other constitutional rights. Today this is status quo.
Spying on allies... is also expect, but there's a catch: you're not supposed to get caught. This might mean avoiding some types of spying that are too risky. As long as everybody uses spies "under the table" so nobody notice, it's hard to accuse each other of impropriety.
If a spy screws up badly and IS caught, it IS going to cause a scandal. Traditionally, this means the spying country is going to have to make some sort of gesture or reparation to patch over the relationship. In extreme cases this could be real payments of cash or goods (rarely, even letting the spy be tried in the foreign court). Modern realpolitik probably requires only a minor concession in a future trade agreement.
This isn't a law or treaty; failure to do something to amend the relationship simply leave the insult/animosity unresolved which is probably bad for future negotiations.
So yes, spying will happen on our European allies. We just weren't supposed to get caught at it. Now that we are, it's on us to patch over that relationship, if we care about the future of those relationships.
There was right of privacy mentioned in the International Covenant on Civil and Political Rights