Here how.
UPDATE 1:
From the comments (jpic) it looks like Firefox >= 25 doesn't like the above syntax anymore. I tested on Firefox 27 and it doesn't work while it still work on Webkit/Chrome.
So here is the new one that should cover all recent browsers. I tested Safari, Chrome and Firefox:
<link rel="icon" href="data:;base64,=">
I left out the "shortcut" name from the "rel" attribute value since that's only for older IE and versions of IE < 8 doesn't like dataURIs either. Not tested on IE8.
UPDATE 2:
If you need your document to validate against HTLM5 use this instead:
<link rel="icon" href="data:;base64,iVBORw0KGgo="