Since variables aren't interpolated (the value doesn't get substituted in) when you use single quotes, your page is probably showing $user instead of Richardtagger, or whatever username you're looking for. So try this:
$user = $_SESSION['username'];
if ($_SESSION['logged_in']) // you don't need the "==1" because if the variable is 1 it will resolve to TRUE inside the conditional
echo '<font face=Tahoma><font color="#FF0000"><strong>You are logged in as' . $user . '</strong></font>';
I took the liberty of closing your HTML tags.
Hope that works a bit better.