Apache 2 `UserDir` problem in OS X Mountain Lion (10.8) Server after upgrade from Lion (10.7)
It seems that the Apache configuration files in /etc/apache2 are not at all considered by the Apache version provided by the Server application.

With the Server application, all configurations are in /Library/Server/Web/Config/apache2

As the ReadMe.txt of this directory says, the default apache configuration file is httpd_server_app.conf, and I just had to uncomment the line Include /private/etc/apache2/extra/httpd-userdir.conf in this file!

problem solved.

[EDIT]
As notified by Kristopher Johnson, it may also be necessary to uncomment LoadModule apple_userdir_module