The ports with a remote address of 0.0.0.0 are listening ports for thing like NETBios and DCOM which are present in all windows machines. On my machine, I also have a VNC program that is listening so that I can connect to all the computers in my home and when Windows Live Messenger is running, an application called livecall.exe is running which monitors for incoming net calls.

Bascially, these services aren't connected to anything, they are just waiting for connections. And that is why we have firewalls, to hide these ports and prevent unauthorised connections which Zone Alarm will be actively doing. This requires no action on your part. A lot of modern routers have firewalls built in which also hide these ports and block attacks.

You can check the visibility of your PCs ports using online remote scanners such as Shields Up!.

Visit the link, click Proceed. Then hit All Service Ports at the bottom. This will perform a remote scan of your PC. If all ports turn green, they are hidden from attack.

This really isn't anything to worry about in most cases.