The following ports need to be enabled to allow the launcher to patch and authenticate, and for the game to play:
All ports listed are the remote ports (MxO servers). The local port varies.
TCP range: 10000 to 11000 (incoming & outgoing traffic)
UDP range: 10000 to 11000 (incoming & outgoing traffic)
TCP port: 7030 (outgoing traffic)
UDP port: 9700 (incoming & outgoing traffic)
You can also allow TCP port 5190. It is not needed at the moment for the game but you may want to leave it on, as it allows AOL chat (ingame chat used to use this, but this has since been disused). If you enable this port don't restrict it to launcher.exe and matrix.exe on your PC's firewall as that will stop AIM, trillian or whatever AOL chat program you use.
I hope this helps those who seem to have constant problems.
I am behind a WatchGuard Firebox firewall. To maintain security on the network I would recommend getting a fixed IP for your machine (get a DHCP reservation if you need to) then allowing those ports to your machine's IP address only. Runing Sygate Personal Firewall on your machine will restrict this access to launcher.exe (and by chaining privelages matrix.exe as well) preventing you from becoming a network backdoor.
December 6th, 2007 UPDATE:
A warning to anyone with nVidia networking hardware. The nVidia network drivers include a firewall application, do not use it. I recently had a machine that was running Windows XP Pro with Sygate Personal Firewall (the same firewall that is in Symantec Internet Security). It required a motherboard replacement and the new board had a nVidia Gigabit NIC (Network Interface Card). The drivers for which included the nVidia firewall. It broke everything.
If you EVER update your nVidia network drivers and are using a software firewall, you will need to reinstall your software firewall after updating the NIC drivers. If you don't your firewall will either do nothing or block everything (unless you set a specific port bypass). Aditionally the nVidia firewall is know to cause problems with a number of games and other networked applications.