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You can add one to your site by making a 16 x 16 pixel gif of your choice, renaming it to "favicon.ico" and uploading it to the root/public/html directory.
If you just want to eliminate 404 errors you can use a transparent one.
If your site supports mobile devices, be aware that Apple's iPhone will ask for "apple-touch-icon.png" or "apple-touch-icon-precomposed.png" in the same way that non-mobile browsers ask for favicon.ico, so you may also want to make a 57x57-pixel image for it as well.
I'm lazy; I make my original image at 57x57 with a 4-pixel border all around, save it as a .png for the Apple devices, then crop it to 48x48 (thus removing the border and one row of pixels from the bottom and left side), and then scale that 48x48 image down both to 32x32 and to 16x16.
Also can someone offer a recommendation for a tool to create multi-sized ico files? I had no idea that one could save an image file with multiple images within it.
This is a free favicon.ico generator that will take a picture from your desktop, resize and format it, and tell you how to implement it into your site. Having used this times before, its definitely a site for your Goodie Bag.
[edited by: brotherhood_of_LAN at 7:59 am (utc) on April 24, 2009]
[edit reason] No URL specifics please, as per the ToS (few exceptions). Thanks [/edit]