Showing and hiding element, making my code more useful
Item 1: I'd suggest getting rid of all global variables except tog.  They don't look like they are needed and just open you up for a potential conflict with other global variables.

Item 2: This line of code:

if (tog = 1 &amp;&amp; clicked != menu) {


should probably be:

if (tog == 1 &amp;&amp; clicked != menu) {


Comparisons are done with == or ===, not with = which is an assignment.

Item 3:  addEventListener() does not exist in versions of IE before IE9, so you will need to use attachEvent() if addEventListener() is not present.

Item 4: Here's a version I've done that gets rid of all globals except tog (which I renamed menuVisble and made it a boolean.  It also uses anonymous functions (less global namespace pollution) for the handlers and makes some other cleanups.  You can see it work here: http://jsfiddle.net/jfriend00/MEaPs/.

var menuVisible = false; // set up a toggle so you can display block and then none.

// listener for any clicks on the document.
document.addEventListener("click", function(e) {
    var clicked = e.target;
    var menu = document.getElementById("menu");
    //check to see if user clicks outside of the
    if (menuVisible &amp;&amp; clicked != menu) {
            menu.style.display = "none";
            document.getElementById("button").innerHTML = "Click Me";
            menuVisible = false;
        }

}, false); 

document.getElementById("button").addEventListener("click", function(e) {
    var menu = document.getElementById("menu");
    e.preventDefault();
    e.stopPropagation();
    if (menuVisible){
        menu.style.display = "none";
        this.innerHTML = "Click Me";
        menuVisible = false;
    } else {
        menu.style.display = "block";
        this.innerHTML = "Opened!";
        menuVisible = true;
    }
}, false);


Item 5:  And here's a version with no globals at all.  It uses the class of the menu to control and discern visibility.  You can see it work here: http://jsfiddle.net/jfriend00/96NfD/.

// listener for any clicks on the document.
document.addEventListener("click", function(e) {
    var menu = document.getElementById("menu");
    var menuVisible = menu.className.indexOf("hidden") == -1;
    //check to see if user clicks outside of the
    if (menuVisible &amp;&amp; e.target != menu) {
            document.getElementById("button").innerHTML = "Click Me";
            menu.className = "hidden";
        }

}, false); 

document.getElementById("button").addEventListener("click", function(e) {
    e.preventDefault();
    e.stopPropagation();
    var menu = document.getElementById("menu");
    var menuVisible = menu.className.indexOf("hidden") == -1;
    if (menuVisible) {
        this.innerHTML = "Click Me";
        menu.className = "hidden";
    } else {
        this.innerHTML = "Opened!";
        menu.className = "";
    }
}, false);