Mountain Lion removes the configuration file that gives web access to your user directory. The configuration files are in
/etc/apache2/users/. The missing one is
user.conf, where user is your short username.
If you don't want to fiddle with the command line, here's an Applescript you can run to create a configuration file for your user. It will ask for your password because it has to create the file in a system-level directory and needs elevated privileges.
In your applications folder or Launchpad, open
Other > Applescript Editor. Copy the script below and paste it into the text area of the Applescript editor. Then click the Run button.
set userHome to (short user name of (system info))
set configFile to "/etc/apache2/users/" & userHome & ".conf"
set configFileContents to "<Directory \"/Users/" & userHome & "/Sites/\">
Options Indexes MultiViews
Allow from all
do shell script "echo '" & configFileContents & "' > " & configFile with administrator privileges
do shell script "/usr/sbin/apachectl restart" with administrator privileges
When the script finishes, you should be able to access your user-level web page.