Check out the Attribute Contains Selector if you're keen on using the ID as the selector. Then you can do something like:
$('input[id*="mycomponentid"]').fadeIn();
Another option is to assign distinct CSS classes to the components you need to interact with in jQuery. I.e.
$('.jsf-username-field').fadeIn();
If you use the later approach, you can allow the framework to generate IDs and you don't even need to bother with them most of the time, especially if you're using a nice AJAX-JSF framework. I favor this approach because it doesn't mingle HTML / JavaScript with JSF.
