First of all, you could change the tomcat listening port to 80 (which I assume is what you have done), but it's not a that good idea, because the port number 8080 is still hardcoded in many files in the webapplication. A better solution would be to put a proxy (an Apache server for instance) in front of Alfresco and let that listen on port 80 and forward requests to Tomcat.
Regarding your main question that is discussed under this topic, where I have presented one solution that will allow users to only enter http://servername/ instead of http://servername/alfresco, but that won't hide the /alfresco (it will be added by Apache):
