Is there any way to get a list of documents and pages within a MOSS 2007 site collection downloaded by a user over, say, the last seven days?
(without using a log file analyser)
I believe you want to look into auditing. Here's something to get you started: http://admincompanion.mindsharp.com/BillBlog/Lists/Posts/Post.aspx?ID=18
MOSS comes with some basic audit reports. Have a look at this resource on Office Online for more details.
Alternatively, have a look at our SharePoint Audit Suite. It is cheap and does exactly what you are after.
I worked on the product so I am obviously biased :-)