Assuming you are running nagios on a UBuntu box and want to disable notification emails for a particular service, you would follow the steps below.
1. Locate the service configuration file. In my case it happened to be located at /etc/nagios3/conf.d/localhost_nagios2.cfg
2. Edit the file and find the service definition for the service you are interested in. The service definitions all start with 'define service'
3. Add the following configuration inside the service definition
4. Restart nagios - /etc/init.d/nagios3 restart
Notification would now be disabled for this service.