This is a great suggestion. I'm getting sick of having to open incongito mode on Chrome unless I want Google Now to happily repeat whatever I was looking at later. Uh, I don't need reminders for sales on hemorrhoid medicine or news alerts about the side effects of MDMA. I don't need that popping up where others can see it.
Some kind of "off the record" mode would be invaluable for voice interfaces. Hell, it would be nice if there was a check box under the Google search box as well, but I imagine Google would never make it too easy to avoid their data mining. I feel like we never had the proper privacy conversation we needed to have with companies like MS, Google, Facebook, etc. I think some level of easy to use yet strict segregation between what I consider my public life and my private life should be cooked-in, and enabled by default, into all this software.