Do you buy a component cable for your HDTV or did you stick with composite?

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The preferred order for video connections are, in general:

1) HDMI/DVI
2) Component
3) SVideo
4) Composite

You should never use composite if you don't have to, especially with an HDTV.  You won't get HD via composite, just 480i.

So for the Wii, get the component cables.  For your cable, use HDMI (make sure you sign up to get HD content).  For your DVDs, use either HDMI (HD/upscale players) or component (standard players).