A good (and simple) solution as pointed out in the comments on the original question is to use the stack property of an Error object like so:
function stackTrace() {
    var err = new Error();
    return err.stack;
}
This will generate output like this:
DBX.Utils.stackTrace@http://localhost:49573/assets/js/scripts.js:44
DBX.Console.Debug@http://localhost:49573/assets/js/scripts.js:9
.success@http://localhost:49573/:462
x.Callbacks/c@http://localhost:49573/assets/js/jquery-1.10.2.min.js:4
x.Callbacks/p.fireWith@http://localhost:49573/assets/js/jquery-1.10.2.min.js:4
k@http://localhost:49573/assets/js/jquery-1.10.2.min.js:6
.send/r@http://localhost:49573/assets/js/jquery-1.10.2.min.js:6
Giving the name of the calling function along with the URL and line number, its calling function, and so on.
I have a really elaborate and pretty solution that I have devised for a project I am currently working on and I have extracted and reworked it a bit to be generalized. Here it is:
(function(context){
    // Only global namespace.
    var Console = {
        //Settings
        settings: {
            debug: {
                alwaysShowURL: false,
                enabled: true,
                showInfo: true
            },
            stackTrace: {
                enabled: true,
                collapsed: true,
                ignoreDebugFuncs: true,
                spacing: false
            }
        }
    };
    // String formatting prototype function.
    if (!String.prototype.format) {
        String.prototype.format = function () {
            var s = this.toString(),
                args = typeof arguments[0],
                args = (("string" == args || "number" == args) ? arguments : arguments[0]);
            if (!arguments.length)
                return s;
            for (arg in args)
                s = s.replace(RegExp("\\{" + arg + "\\}", "gi"), args[arg]);
            return s;
        }
    }
    // String repeating prototype function.
    if (!String.prototype.times) {
        String.prototype.times = function () {
            var s = this.toString(),
                tempStr = "",
                times = arguments[0];
            if (!arguments.length)
                return s;
            for (var i = 0; i < times; i++)
                tempStr += s;
            return tempStr;
        }
    }
    // Commonly used functions
    Console.debug = function () {
        if (Console.settings.debug.enabled) {
            var args = ((typeof arguments !== 'undefined') ? Array.prototype.slice.call(arguments, 0) : []),
                sUA = navigator.userAgent,
                currentBrowser = {
                    firefox: /firefox/gi.test(sUA),
                    webkit: /webkit/gi.test(sUA),
                },
                aLines = Console.stackTrace().split("\n"),
                aCurrentLine,
                iCurrIndex = ((currentBrowser.webkit) ? 3 : 2),
                sCssBlack = "color:black;",
                sCssFormat = "color:{0}; font-weight:bold;",
                sLines = "";
            if (currentBrowser.firefox)
                aCurrentLine = aLines[iCurrIndex].replace(/(.*):/, "$1@").split("@");
            else if (currentBrowser.webkit)
                aCurrentLine = aLines[iCurrIndex].replace("at ", "").replace(")", "").replace(/( \()/gi, "@").replace(/(.*):(\d*):(\d*)/, "$1@$2@$3").split("@");
            // Show info if the setting is true and there's no extra trace (would be kind of pointless).
            if (Console.settings.debug.showInfo && !Console.settings.stackTrace.enabled) {
                var sFunc = aCurrentLine[0].trim(),
                    sURL = aCurrentLine[1].trim(),
                    sURL = ((!Console.settings.debug.alwaysShowURL && context.location.href == sURL) ? "this page" : sURL),
                    sLine = aCurrentLine[2].trim(),
                    sCol;
                if (currentBrowser.webkit)
                    sCol = aCurrentLine[3].trim();
                console.info("%cOn line %c{0}%c{1}%c{2}%c of %c{3}%c inside the %c{4}%c function:".format(sLine, ((currentBrowser.webkit) ? ", column " : ""), ((currentBrowser.webkit) ? sCol : ""), sURL, sFunc),
                             sCssBlack, sCssFormat.format("red"),
                             sCssBlack, sCssFormat.format("purple"),
                             sCssBlack, sCssFormat.format("green"),
                             sCssBlack, sCssFormat.format("blue"),
                             sCssBlack);
            }
            // If the setting permits, get rid of the two obvious debug functions (Console.debug and Console.stackTrace).
            if (Console.settings.stackTrace.ignoreDebugFuncs) {
                // In WebKit (Chrome at least), there's an extra line at the top that says "Error" so adjust for this.
                if (currentBrowser.webkit)
                    aLines.shift();
                aLines.shift();
                aLines.shift();
            }
            sLines = aLines.join(((Console.settings.stackTrace.spacing) ? "\n\n" : "\n")).trim();
            trace = typeof trace !== 'undefined' ? trace : true;
            if (typeof console !== "undefined") {
                for (var arg in args)
                    console.debug(args[arg]);
                if (Console.settings.stackTrace.enabled) {
                    var sCss = "color:red; font-weight: bold;",
                        sTitle = "%c Stack Trace" + " ".times(70);
                    if (Console.settings.stackTrace.collapsed)
                        console.groupCollapsed(sTitle, sCss);
                    else
                        console.group(sTitle, sCss);
                    console.debug("%c" + sLines, "color: #666666; font-style: italic;");
                    console.groupEnd();
                }
            }
        }
    }
    Console.stackTrace = function () {
        var err = new Error();
        return err.stack;
    }
    context.Console = Console;
})(window);
Check it out on GitHub (currently v1.2)! You can use it like Console.debug("Whatever"); and it will, depending on the settings in Console, print the output and a stack trace (or just simple info/nothing extra at all). Here's an example:

Make sure to play around with the settings in the Console object! You can add spacing between the lines of the trace and turn it off entirely. Here it is with Console.trace set to false:

You can even turn off the first bit of info shown (set Console.settings.debug.showInfo to false) or disable debugging entirely (set Console.settings.debug.enabled to false) so you never have to comment out a debug statement again! Just leave them in and this will do nothing.