Edit in JSFiddle

// A few functions with some calls between them
var obj = { someCoolFunction: function () { // Do some action 
            },
            anotherFunction: function () {  // Do some action 
            },
            thirdFunction: function () {    // Do some action 
                obj.anotherFunction();
            },
            fourthFunction: function () {   // Call anotherFunction and someFunction
                obj.anotherFunction();
                obj.someCoolFunction();
            },
            allFunction: function (e) {
                obj.someCoolFunction(e);
                obj.anotherFunction(e);
                obj.thirdFunction(e);
                obj.fourthFunction(e);
            }
}

function WrapFunctions() {
    // Run over all objects in the obj
    for (fnc in obj) {
        if (typeof obj[fnc] == "function") {
            var currentelement = $("#debuglog");
            (function (originalFnc, name) {
                // Redefine the function
                obj[fnc] = function () {
                    // Write the function name in an LI and nest 
                    // deeper function calls in a UL
                    var fncItem = $("<li>Called " + name + "</li>")
                    var newparent = $("<ul></ul>");
                    currentelement.append(fncItem.append(newparent));
                    var olditem = currentelement;
                    currentelement = newparent;
                    
                    // Call the original function
                    originalFnc.call(this, arguments);

                    // Reset the current container
                    currentelement = olditem;
                };
            })(obj[fnc], fnc);  // Pass in the original function and its name
        }
    }
}WrapFunctions();
$("#btnAction1").click(obj.someCoolFunction);
$("#btnAction2").click(obj.anotherFunction);
$("#btnAction3").click(obj.thirdFunction);
$("#btnActionAll").click(obj.allFunction);

Click the buttons to see the call stack viewer in action<br />
<input type="button" value="Do Action 1" id="btnAction1" />
<input type="button" value="Do Action 2" id="btnAction2" />
<input type="button" value="Do Action 3" id="btnAction3" />
<input type="button" value="Do All Actions" id="btnActionAll" />
<ul id="debuglog"></ul>

#debuglog{
            width: 300px;
            position: absolute;
            z-index: 1001;
            right: 10px;
            top: 20px;
            box-shadow: 3px 3px 15px 3px #000;
            width: 312px;
            padding: 10px;
            height: 400px;
            overflow: auto;
            }
        #resultItems ul{
            margin-top: 0px;
            padding-left: 10px;
            margin-bottom: 0;
            }
        #resultItems li{
            list-style-type: none;
            cursor: pointer;
            }