It would also be an obvious privacy violation for the NSA to install cameras in our bedrooms, even if they promised to never watch the video without a warrant.
Yes, but that's because it would require access to your bedroom, not because it's evil to capture data per se.
What if, instead, you had a bedroom camera (maybe for tracking frisky escapades) and it streamed wirelessly to a home server? The more relevant question then becomes whether it's OK for the NSA (or rather, FBI) to sit on the street and capture that WiFi stream from a public road.
As you consider this question, also consider how many open WiFi hotspots you've ever used (or broke the WEP for) in your hacking career. :) The idea that it's OK to hack the stupid because their system was so open to attack might finally die due to PRISM, if people are intellectually honest with themselves.
I think there's a significant difference between using an open (or even poorly secured, although I've never done that) hotspot in order to get onto the internet, vs deliberately capturing personal data from that hotspot with the intention to analyze it and possibly use it to harm the subjects of that data.