Me too now: iPhone 4, original Apple Cable, Windows 7 Ultimate, latest iTunes - and get "Trust This Computer" most every time I plug in, or reboot (I'm a developer and do the latter frequently). It *MAY* not have happened with iOS 7.0.0, but definitely DOES with iOS 7.0.2.
This is NOT an iTunes problem - and so (even though I tried it), there is no point in "reparing" Apple Device Supprot, etc. The message appears EVEN BEFORE WINDOWS BOOTS - or if I boot into another O/S that does not include iTunes.
It IS an IOS 7 PROBLEM. And its yet another PITA.
Apple have SERIOUSLY screwed up with iOS 7 (still having issues with getting FaceTime to work).
If only Steve Jobs was still with us ... I remember thinking the iOS 6 Apple Maps debacle was a foretaste of things to come. iOS 7 is just proving that we've seen the best already.