You'll have to insert a disc that isn't your favorite game when you first fire up your Wii. UPDATE: Not anymore (At least in the US).
Update 11/10 -
The latest version of the console that we have seen does not come with a startup disc as previously reported. The system starts up with no update required.
Original Story 11/4 -
Joystiq is reporting that a startup disc that is packaged with Wii is required when first starting up the system. While the reason is unknown at this time, there are several possibilities. Some people think it is a last minute firmware update, meaning that Wiis were being manufactured before the firmware was finalized. There is also the possibility that it is just a tutorial disc that shows players how to get started with the system. Given that the initial request is written to the screen in three different languages, it is possible that the disc only copies the files needed for the player's spoken language. This would help keep unneeded information out of the precious 512 megabytes of memory in the system.
If the disc is more than a system tutorial (which is very likely), this would prove that the firmware in the system is modifiable in some way and that this can be done with a disc. In order to update Wii units that aren't connected to the Internet, it is possible that Nintendo could release similar discs at retail or bundle them with games in the future.
For a picture of the error message, check out Joystiq's article in the related link field above.