.not accepts a selector, including a selector group. So:
$('a').not('[href="#"], [href="#navShow"], [href="#navHide"], [href="#about"]').click(function () {
});
Or with :not instead (CSS docs, jQuery docs):
$('a:not([href="#"]):not([href="#navShow"]):not([href="#navHide"]):not([href="#about"])').click(function () {
});
(Unlike .not, :not cannot accept a selector group, only a simple selector. But we can chain them within the overall selector.)
That said, you might consider adding a class to the a elements you do or do not want selected for this, and using that class (with or without not depending on which way you go) instead of doing this href check individually.