This doesn't come up all that often, but - say you had your Wii plugged into a TV that supports progressive scan and had that enabled. Then you switch TVs to one that doesn't. Think something like bringing the Wii over to a friend's house. This only applies when using the Component cables (red, green, and blue video plugs) - the Composite cable (single yellow plug) doesn't support 480p and the Wii won't try it. Which is why the following works.
The PS3 is nice enough to provide a feature where holding down the power button resets it to 480i. The Wii does not.
But there's still a very simple way to reset it to 480i mode: unplug the component cable before turning the Wii on. (From the Wii, since that's one plug, although removing all three component cables from the TV should work too.)
Important note: This just starts it in 480i mode. This does not disable 480p mode! Immediately go into the System menu, select Wii Settings, System, and Resolution to change back to 480i mode. If you don't, the next time you start a 480p-capable game, it will switch to 480p.