Some people are saying their Wii cannot connect to wifi using a Linksys wireless router, in that case, you can buy the following:
If you want to use the online features of your Nintendo DS or Wii console and you don't have a wireless router, you can use the Nintendo Wi-Fi USB Connector.
The Wi-Fi USB Connector is a dedicated wireless access point that plugs into a USB port on your PC. It uses your PC to access your existing high-speed internet connection. Multiple systems may be registered to the USB Connector and up to five (5) systems can be connected wirelessly at the same time. The Nintendo Wi-Fi USB Connector will ONLY work with the Nintendo DS and/or Wii console system.
Nintendo: Online Store - Product Detail