Seems there is a bit of an issue with the MSDN Product Keys for Office 2007.
Several of the Office products share the same Product Key issued by MSDN; "Office 2007 Desktop Programs" is used for Groove. InfoPath, and OneNote and both Project and Visio share another one.
When I went to activate the assorted application on my workstation it failed for InfoPath, OneNote, and Project (Groove and Visio activated without a hitch). After some looking around I was able to find a thread in the managed MSDN newsgroups on this topic. Looks like several users have reported this problem.
My guess is that the licensing servers are unable to recognize which product is being activated and it assumes that you are trying to re-activate the same product again and again. They also don't seem to know these are MSDN keys that should be allowed several installations (see MSDN Licensing FAQ)
I was able to get OneNote activated over the phone (it was the only application I needed ASAP) after I explained the problem. Of course your mileage may vary.
Update: This seems to have been fixed. Also, I've turned comments off due to people using the comments to request and publish product keys. Go pirate somewhere else guys.