Update for September 2014
<link rel="shortcut icon" sizes="196x196" href="icon-196x196.png">
is initially what you need to allow Chrome for Android to have a "Add to home screen" option show up in the settings.
A starting template like
<!doctype html>
<html>
<head>
<title>HTML5 app</title>
<link rel="shortcut icon" sizes="128x128" href="./icns/1410745473_39412.ico">
<meta name="mobile-web-app-capable" content="yes">
<meta name="apple-mobile-web-app-capable" content="yes">
</head>
<body>
<h1>Adventures in HTML5 android apps</h1>
</body>
<script type="text/javascript">
navigator.standalone = navigator.standalone || (screen.height-document.documentElement.clientHeight<40)
alert(navigator.standalone == true);
alert(screen.height-document.documentElement.clientHeight)
</script>
</html>
Works with the latest Chrome for Android app ( version 35 ).
Add https://stackoverflow.com/users/67606/pablo-santa-cruz's answer and that should be iOS compatible as well ( I no longer own any iOS devices so I am not 100% sure ).