We have received a number of queries in the past asking about QTP support for Windows 7. For some, windows 7 used to work normally while not quite properly for others. Our standard answer was “There is no official word from HP yet”. No more.
Just two days back (7th/Dec), HP announced the support for Windows 7 and Windows Server 2008 R2 for QTP10. (Though there is no such information about the versions of QTP prior to 10.0) You would need to download this patch (requires HP support login). More details about this patch are available on HP support site.
To be updated on such news, you can subscribe to receive email notification about patch updates from inside your HP support account OR this blog.
Also, check the complete support matrix of various Windows versions vs QTP versions.