Ezekiel: you are missing the point, as people have before you. Ignore the whole IP address issue. Moderators have closed other issues where it has been stated we can not connect at all. Those issues have been marked as duplicates of this one, and people have been directed here for all LAN world connection issues.
Maybe the IP display is working as designed, but the fact is that people can not connect. It's not that we see 0.0.0.0 and are left puzzled as to whether or not to select that connection. It's that when we attempt to connect, we are told "connection refused" or some other message that means we're simply not connected to the LAN world as attempted.
Are you SURE that this is resolved? Because there appears to be a whole lot of "Can't connect to LAN worlds" wrapped up with this "Why does it say 0.0.0.0?" issue. I think someone was far too aggressive in marking LAN world connection issues as duplicates of this 0.0.0.0 issue.
I have to retract my comment that it's working now. Still can't connect in 1.4.5. Should this be re-opened, as the fix does not appear to resolve the bug for everyone?
If it's still not working for you with the 1.4.5 update, here are a couple of things I did (Windows 7 64-bit):
uninstalled both 32-bit and 64-bit Java
installed latest version of 32-bit Java (Java 7 update 9)
I can now connect to and host LAN worlds (although starting a LAN world still displays the incorrect 0.0.0.0 IP address).
I don't know if it was getting rid of 64-bit Java or simply updating 32-bit Java that did the trick. Perhaps try simply updating your Java first, to see if that gets you going.
GrygrFlzr: for your question about typing the real local address of the server, I wasn't typing an address at all. Someone else in my home starts a world and opens it to LAN. I can see the LAN world in my Multiplayer screen, but clicking it displays a message "Connecting to the server..." that eventually changes to "Failed to connect to the server Connection timed out: connect"
Trying a Direct Connection to the IP address shown in the LAN world selection (a 192.168. address) has the exact same result.