I'd suggest:
function toggle(el, message1, message2) {
    if (!el || !message1 || !message2) {
        return false;
    }
    var text = el.tagName.toLowerCase() == 'input' ? el.value : (el.textContent || el.innerText),
        newText = text == message1 ? message2 : message1;
    if (el.tagName.toLowerCase() == 'input') {
        el.value = newText;
    }
    else {
        el.firstChild.nodeValue = newText;
    }
}
document.getElementById('idButton').onclick = function(){
    toggle(this, 'Show', "Don't show");
};
JS Fiddle demo.
A slightly revised version of the above:
function isTag(el, tagname) {
    if (!el || !tagname) {
        return false;
    }
    else {
        return el.tagName.toLowerCase() == tagname.toLowerCase() ? true : false;
    }
}
function toggle(el, message1, message2) {
    if (!el || !message1 || !message2) {
        return false;
    }
    else {
        var isInput = isTag(el, 'input'),
            text = isInput ? el.value : el.textContent || el.innerText,
            newText = text == message1 ? message2 : message1;
        if (isInput) {
            el.value = newText;
        }
        else if (el.textContent) {
            el.textContent = newText;
        }
        else {
            el.innerText = newText;
        }
    }
}
document.getElementById('idButton').onclick = function(){
    toggle(this, 'Show', "Don't show");
};
JS Fiddle demo.