Is there a way I can tell (other than in the SVN Log...because it only shows me if someone committed) who has updated recently so that I know they have downloaded my code? I'm looking specifically into updates (not commits which can obviously be seen in SVN Log).
Sure - run your own subversion server, turn on logging, and read the logs.
Edit: TortoiseSVN is a client. Subversion is a server. Imagine Tortoise being a browser (firefox) and Subversion being the webserver (apache or IIS). What you want to do is read the server logs from Subversion (not the SVN Log, which is something completely different).
I don't know who or how you run your svn server. I run svnserve on linux through apache (so I say https:// instead of svn://), and I can read subversion logs through apache. They look like this:
[18/Oct/2009:14:21:41 -0400] xx.xx.xx.xx TLSv1 DHE-RSA-AES256-SHA "OPTIONS /svn/terracidal/root HTTP/1.1" 401
[18/Oct/2009:14:21:42 -0400] xx.xx.xx.xx TLSv1 DHE-RSA-AES256-SHA "OPTIONS /svn/terracidal/root HTTP/1.1" 401
[18/Oct/2009:14:21:45 -0400] xx.xx.xx.xx TLSv1 DHE-RSA-AES256-SHA "OPTIONS /svn/terracidal/root HTTP/1.1" 194
[18/Oct/2009:14:21:45 -0400] xx.xx.xx.xx TLSv1 DHE-RSA-AES256-SHA "PROPFIND /svn/terracidal/root HTTP/1.1" 696
Again, these are server logs, not the SVN Log. I can crack up logging verbosity and see connections, debug statements, things about the running of the server - but also things like who's connecting and performing operations. That's what you care about. So if you or your company runs their own svn server, ask the admin if they can make the logs available for reading. If you use a 3rd party, you're probably out of luck.