animateScrollTo.js

(function () {
    var requestAnimFrame =  window.requestAnimationFrame ||
                            window.webkitRequestAnimationFrame ||
                            window.mozRequestAnimationFrame ||
                            window.oRequestAnimationFrame ||
                            window.msRequestAnimationFrame ||
                            function (callback) {
                                setTimeout(callback, 1000 / 60);
                            },
        easing = {
            linear: function (t) { return t; },
            easeInQuad: function (t) { return t * t; },
            easeOutQuad: function (t) { return t * (2 - t); },
            easeInOutQuad: function (t) { return t < 0.5 ? 2 * t * t : -1 + (4 - 2 * t) * t; },
            easeInCubic: function (t) { return t * t * t; },
            easeOutCubic: function (t) { return (--t) * t * t + 1; },
            easeInOutCubic: function (t) { return t < 0.5 ? 4 * t * t * t : (t - 1) * (2 * t - 2) * (2 * t - 2) + 1; },
            easeInQuart: function (t) { return t * t * t * t; },
            easeOutQuart: function (t) { return 1 - (--t) * t * t * t; },
            easeInOutQuart: function (t) { return t < 0.5 ? 8 * t * t * t * t : 1 - 8 * (--t) * t * t * t; },
            easeInQuint: function (t) { return t * t * t * t * t; },
            easeOutQuint: function (t) { return 1 + (--t) * t * t * t * t; },
            easeInOutQuint: function (t) { return t < 0.5 ? 16 * t * t * t * t * t : 1 + 16 * (--t) * t * t * t * t; }
        },
        stopped = false,
        animating = false;

    window.animateScrollTo = function (Y, duration, easingKey, callback) {
        
        var start = Date.now(),
            elem = (typeof document.documentElement.scrollTop !== 'undefined') ? document.documentElement : document.body,
            from = elem.scrollTop;

        if (from === Y && callback) {
            callback();
            return; /* Prevent scrolling to the Y point if already there */
        }

        function min (a, b) {
            return a < b ? a : b;
        }

        function scroll () {
            var currentTime = Date.now(),
                time = min(1, ((currentTime - start) / duration)),
                eeasedT = (easing[easingKey] || easing.linear)(time);

            if (stopped) {
                stopped = false;
                return;
            }

            animating = true;

            elem.scrollTop = (easedT * (Y - from)) + from;

            if (time < 1) {
                requestAnimFrame(scroll);
            } else if (callback) {
                callback();
            }
        }

        requestAnimFrame(scroll);
    };

    window.stopScrollTo = function () {
        stopped = true;
    };

}());

example.js

window.addEventListener('load', function () {

    animateScrollTo(1000, 3000, 'easeOutQuart');

    setTimeout(function () {
        stopScrollTo();
        animateScrollTo(0, 3000, 'easeInOutQuart');
    }, 500);
});

Beautifully coded, but contains an error and a mistype.

elem = (typeof document.documentElement.scrollTop !== 'undefined') ? document.documentElement : document.body,

Failed in at least Chrome on a Mac though I don't know why as typeof document.documentElement.scrollTop equals number.
Replacing with the original:

elem = document.documentElement.scrollTop ? document.documentElement : document.body,

Only works in non IE - rubbish.

Typo line 46: eeasedT

Currently working on a solution.