Steve Kondik, one of the driving forces behind the CyanogenMod custom rom for Android, via its Google+account, and let them know that there is working on a ‘incognito mode’ for individual apps in the custom rom.
The incognito mode will be easy to enable via the information page of individual apps. Contentaanbieders can choose whether they have the api support. Kondik states explicitly that the feature is intended to block ads or to change the imei to spoof, but only to the personal data of users to protect. It is not yet sure that the feature actually will find its way to CyanogenMod.