How can I run some JavaScript *after* a form submit event?

This is pretty much the same as sp00m's answer, except it uses Javascripts native submit to prevent the recursive call.

$('#myForm').submit(function() {
    this.submit();
    disableFields(); // your own function
    return false;
});

Don't allow further submits by disabling the submit buttons, you don't need to do anything else. Alternatively, hide the form and replace it with something that spins so users are mesmerized into thinking that Something Important is happening.