The Firefox 4 beta includes a "Feedback" button in it. It periodically throws up pop-ups inviting me to participate in surveys, or to ask me to send some anonymized data that they've gathered based on my usage patterns:
If I click the Feedback button, I'm given the ability to say "Firefox made me happy, because..." or "Firefox made me sad, because..." and these results are all collated at http://input.mozilla.com/en-US/. I can also view all data I've sent, or tell them to stop bugging me with pop-ups. :)
I think something like this for Drupal 8 would be awesome, particularly during dev releases. I'm not sure if we could get away with it in a production release -- there are privacy considerations and other things. But it would help us resolve questions like "How many people use this buggy-assed version of MySQL?" and "How many sites actually use Poll module?" etc.
Obviously, though, there's a lot more to this than someone whipping up a module to add a button to the toolbar. We'd need pretty significant infrastructure behind the scenes to do the push notifications, requirements gathering, etc. Something like http://drupal.org/project/uts might be useful as a starting point? Not sure. We also obviously need a way to map random "makes me sad because.." to real bug reports, which either requires a small army of humans or some insanely smart pattern matching.
If it was developed in a general way though (much like our integration testing infrastructure, except installable by mere mortals ;)), I think it'd be a huge boon to Drupal as a platform. Like Update Status module, we could make it configurable so that instead of them pinging http://feedback.drupal.org/whatever, they could use the same tools to ping http://feedback.example.com/whatever.
Anyway, just wanted to log this here for later while it was on my mind.