I run Apache 1.x right now, and can't switch to Apache 2.0 just to serve Subversion repositories. Does that mean I can't run a Subversion server?

No, you can run svnserve as a Subversion server. It works extremely well.

If you want WebDAV and all the other "goodies" that come with the Apache server, then yes, you'll need Apache 2.0. It's always an option to run Apache 2.0 on a different port while continuing to run Apache 1.x on port 80. Different versions of Apache can happily coexist on the same machine. Just change the Listen directive in httpd.conf from "Listen 80" to "Listen 8080" or whatever port number you want, and make sure to specify that port when you publish your repository URL (e.g., http://svn.mydomain.com:8080/repos/blah/trunk/).