For UNIX :
One might encounter some problems with sessions, having different sites on the same server : sessions would either merge if one is using more than one site at a time or crash if sites are owned by different system users. For instance :
www.example.com is stored in /home/site1/www
www.example.net is stored in /home/site2/www
Using both www.example.com and www.example.net would cause sessions to act weird.
If you're using PHP as an Apache module, you can easely use php_value in the http.conf to set a unique session.name depending on the site. If you're using suPHP though (PHP as CGI) you can't use php_value, though you can use suPHP_ConfigPath.
Here's an example :
<VirtualHost 10.10.10.10:8081>
DocumentRoot /home/site1/www
ServerName www.example.com
suPHP_ConfigPath /home/site1/server_config
</VirtualHost>
<VirtualHost 10.10.10.10:8082>
DocumentRoot /home/site2/www
ServerName www.example.net
suPHP_ConfigPath /home/site2/server_config
</VirtualHost>
Each server_config folder contain a php.ini file specific to the vHost. You then just have to change the values of each session.name to unique ones and you're done !