However, it seems it can become a bit more complicated once you consider other/mobile platforms (and higher resolution displays)
See http://realfavicongenerator.net/ to generate multiple versions for each platform given a high resolution base file. The code Real Favicon Generator suggests to put in the headers is:
<link rel="apple-touch-icon" sizes="57x57" href="/apple-touch-icon-57x57.png">
<link rel="apple-touch-icon" sizes="114x114" href="/apple-touch-icon-114x114.png">
<link rel="apple-touch-icon" sizes="72x72" href="/apple-touch-icon-72x72.png">
<link rel="apple-touch-icon" sizes="144x144" href="/apple-touch-icon-144x144.png">
<link rel="apple-touch-icon" sizes="60x60" href="/apple-touch-icon-60x60.png">
<link rel="apple-touch-icon" sizes="120x120" href="/apple-touch-icon-120x120.png">
<link rel="apple-touch-icon" sizes="76x76" href="/apple-touch-icon-76x76.png">
<link rel="apple-touch-icon" sizes="152x152" href="/apple-touch-icon-152x152.png">
<link rel="icon" type="image/png" href="/favicon-196x196.png" sizes="196x196">
<link rel="icon" type="image/png" href="/favicon-160x160.png" sizes="160x160">
<link rel="icon" type="image/png" href="/favicon-96x96.png" sizes="96x96">
<link rel="icon" type="image/png" href="/favicon-16x16.png" sizes="16x16">
<link rel="icon" type="image/png" href="/favicon-32x32.png" sizes="32x32">
<meta name="msapplication-TileColor" content="#da532c">
<meta name="msapplication-TileImage" content="/mstile-144x144.png">
I'm guessing that if we really want to do this, in addition of placing a favicon-{StoreId}.ico in the root folder, we could place the corresponding files (maybe a sub directory per store?) and add these headers. Is there a way to add per-store headers?