<p>I've noticed on bank websites, etc, my user IDs aren't saved (they don't appear in a dropdown like other commonly entered stuff does) and there's no prompt for it to remember your password. How is this done? How do the sites notify the browser that they are in 'special' or else exceptions? Just curious.</p>

Usually you just need to put the autocomplete="off" into the form or field you want to block.
Keep in mind that users can get around this with a scriptlet, plugin, or grease-monkey script.
https://developer.mozilla.org/en/How_to_Turn_Off_Form_Autocompletion#Exceptions_and_Recommended_Workarounds
http://msdn.microsoft.com/en-us/library/ms533032(VS.85).aspx