That may change soon as Nintendo is rumoured to be working on USB storage functionality. The back of the Wii console has USB ports but the use of these is pretty limited. When I just had my Wii I wanted to test the Internet by connecting a LAN adapter to one of the USB ports but it didn't work, I later found out on the Internet that only a select amount of LAN adapters, including one from Nintendo, work on the Wii.
eSOL announced this week that it has licensed its PrFILE2 file system and its PrUSB/HOST USB host stack to Nintendo. The company didn't say what Nintendo plans to do with this but it's rumoured that Nintendo may be working on support for USB memory sticks. Or, another possibility is that the firm is working on an external hard drive for the Wii.