Pasa que el tipo de innerHTML es String. Probá así:
Código PHP:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" />
<title>Documento sin título</title>
</head>
<body>
<script>
function suma(x){
var y=parseInt(x)+1;
document.getElementById('total').innerHTML = y;
}
</script>
<div id="total" onclick="suma(this.innerHTML)">0</div>
</body>
</html>