The lead console
HD Pro Component Cables
You can find an HDMI adapter at any electronics store, but if you want the best quality from component cables, the HD Pro Component Cables are well-reviewed by Amazon. These cables are super cheap as they've been drastically reduced in price. And many people report superior quality than the standard composite cables. It won't get rid of the "jaggies", but the image overall will be sharper and will prove to be a valuable purchase.
How to connect
Anyway, after grabbing your HDMI adapter (if you're still taking that route), simply plug in your component cables into the system like normal, then connect the other ends to the adapter, making sure the colors correspond to each other (red, green and blue). Finally, plug your HDMI adapter cable into your HDTV and you're done with your connections. If you haven't already, make sure the Wii is set for 480p output or else the image won't look any different.
If you wanted to save on room, there's HDMI cable for Wii, specifically designed for the console from a 3rd party business. It's called the Wii2HDMI adapter. Again, don't expect to be wowed by a higher resolution, as it's impossible, only 480p remember. It'll just save you more room than an HDMI adapter will giving you the same image quality. Cost wise, it's about the same as well.