On/off are already interpretations for the checkbox having an attribute 'checked' or not. I found this article quite helpful:

http://jquery-howto.blogspot.com/2008/12/how-to-check-if-checkbox-is-checked.html

You can of course always create your own attributes, say whenever someone modifies the state of your checkbox control you'll set that value to whatever you like, e.g.

$('input#myCheckbox').attr('checked'){

  $('input#myCheckbox').attr('myOwnValue', 'This is checked now!');

} else {

  $('input#myCheckbox').attr('myOwnValue', 'Nothing checked here!');

}

[code written out of top of my head, will most likely not work as is]

Of course this would invalidate your html, but you can probably live with that if you so want (and need).

Cheers,

Sascha