I noticed that this is a frequent problem with Wii users and this particular modem. By chance I was assisting my friend with trying to get his Wii connected to this model modem, and also noticed on the Nintendo website this modem was listed as an incompatible modem, but I didn't let that discourage me, and I found a solution!
The following is a workaround in order to get the Wii to connect to the internet through Linksys WCG200-CC ver 2 (similar models please give feedback on whether this works for you).
Find and locate the Wii's MAC address, and write it down. On a computer that's connected wirelessly through the router in question.. Start, Settings, Control Panel, Network Connections. Right click the NIC (Network Card, the one that's currently connected) and hit Properties. Under "General" tab, click the "Configure" button. Click "Advanced" tab. Find "Network Address" or "Locally Administered Address" in the list. In the "Value" box, put in the Wii's MAC address, without dashes. Hit OK, reboot if needed.
What this does is report the computer's MAC as the Wii MAC. With the valuable information my friend provided, I found with this particular router the firewall blocks certain wireless connections. It can be bypassed in the router properties by adding the MAC address to the allowed wireless connections, but manually adding MAC addresses is blocked, for what reason I have NO IDEA. It personally makes little sense to me. But I reasoned that wireless PCs can connect without problems, so if you change the PC's MAC address, it'll be added to the router's MAC list.
To continue and confirm everything worked, access the router settings, which would be "Wireless Access Filter" on this model, click the "Connected Wireless Devices" button, click the "Add" button that's next to the Wii's MAC address, and click Apply. Everything should be set at this point, you can go ahead and change the computer back to its original MAC Address. Connect the Wii using auto configure IP and DNS.
I'm still uncertain if this trick will work with computers hardwired to the router. Perhaps someone can test it for me?
I hope this makes some Wii users happy! Let me know how it works out.