I just got a 42" LCD and I've left my Wii plugged in via composite.  Everywhere I have been where I've seen the Wii connected to a hi-def screen with composite cables I don't like the image.  The sharpness seems to accentuate jaggies and such.  The composite cable in 480i on my LCD looks pretty good and the little bit of "blur" reduces the aliasing some by having no-so-sharp edges.

I'm curious what others have done... Please don't chime in unless you have an HD TV and you have tried both component and composite enough to provide an informed opinion.  This isn't flamebait... 

EDITED:

In general if the source has a component connection or an hdmi connection I would definitely use them vs composite.

My sdtv had a noticeable difference between the composite and component cables, I'm sure your hdtv would as well. 

Man, I have an HDTV - 22" LCD - and a projector and I have went VGA, Component and Composite on my regular TV. By far, the component cables FTW every time. I don't use composite at all unless I have to. Shoot, I even use an HDMI to DVI cable for my HD DVR to my LCD.

It's the only way to watch HD ... component or HDMI ...

Well I have a 46" Sharp Aquos and I plugged my Wii and my 360 to it, my HDTV can show up to 1080i but I looked at a friend 42" Full HDTV(1080p) and there is mostly no difference at all. My Wii a different case, my Wii looks worse on my HDTV with composite than plugged to my 42" SDTV, so I bought the component cables for my wii and the diffence is quite notable but some games doesnt have the 480p 16:9 feature(damn you RE 4). But in games like MP 3 you will be glad that you bought the component cables for it. So buy the component cables for your Wii now!

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). 

I used the composite and thought it looked good. I only have 1 component connection which is currently being used by the 360.

Get component cables.

What? 

Component absolutely! You'll get much improvement especially when you're playing Mario Galaxy. I was comparing with composite a few days ago and the GFX gave me for the very first time a headache, so switched to the component ASAP by seeing the flawless, beautiful graphics again on my 26inc LCD TV ;) I could see Mario blinking with his eyes again *lol*

@Entroper, that's right, Harvest Moon Yasuragi no Ki, which I have, doesn't support 480p either.  

Get HDMI. If not then component.
Don't mess with composite, that''s just ruining the point of having an HDTV. Also, if your playing games through composite you might see a noticeable frame delay.