Note: Instead of doing everything below, you could just restore the backup of your httpd.conf that the Mavericks install created at
/etc/apache2/httpd.conf~previous. Wish I knew that 8 hours ago.
Because I like shiny new things, I decided to upgrade to Mavericks (OS X 10.9) last night. The upgrade finished around 1am, at which point I was tired, so I went to sleep. I woke up this morning to start my day, only to realize that all of my Apache Virtual Hosts were throwing 403: Forbidden errors. After a couple hours of chmod, chown, editing conf files and banging my head against the wall, I finally got it working. So if this happened to you, hopefully the following steps will help.