This is what I'm attempting to achieve:
example1.com > site1
example2.com > site 2

I've created the sites as virtual hosts:
/etc/apache2/sites-available/example1
Code:
<VirtualHost *:80>
        ServerAdmin me@example1.com
        ServerName example1.com
        ServerAlias example1.com
        DocumentRoot /home/me/Sites/example1/www
        <Directory /home/kristian/Sites/example1/www/>
                Options Indexes FollowSymLinks MultiViews
                AllowOverride None
                Order allow,deny
                allow from all
        </Directory>
</VirtualHost>
The www folder has permissions 755, owner me and group me.
The index.html file has permissions 644, owner me and group me.

Visiting the sites shows:
http://example1.com/ & http://example1.com/index.html
Code:
Forbidden

You don't have permission to access / on this server.

Apache/2.2.14 (Ubuntu) Server at pluginstudios.co.uk Port 80
Without the virtual hosts the setup works fine.

Any suggestions please?