Limitations
The Wii has no HDMI output, so you can't use an HDMI cable to connect it to a television.
Options
If you want a slightly higher definition picture than the Wii's standard cable gives you, you can buy a component cable specially designed for the Wii. As with the standard cable, the component cable may only be used with the Wii.
Significance
Because it lacks an HDMI output, the Wii could not display at 1080p (full HD) even if its internal graphics processor was upgraded.
Speculation
Internet rumors have anticipated the release of an "HD Wii" in since 2008. As of 2010, Nintendo has repeatedly refused to confirm the shipping date for such a console.
Benefits
While the lack of HD capabilities may not be ideal for those who own an HDTV, it is in some ways beneficial for owners of standard definition televisions, who need not purchase a new television to fully appreciate Wii games.