Use the modern version of the Fisher–Yates shuffle algorithm:

/**
 * Shuffles array in place.
 * @param {Array} a items An array containing the items.
 */
function shuffle(a) {
    var j, x, i;
    for (i = a.length - 1; i > 0; i--) {
        j = Math.floor(Math.random() * (i + 1));
        x = a[i];
        a[i] = a[j];
        a[j] = x;
    }
    return a;
}

ES2015 (ES6) version

/**
 * Shuffles array in place. ES6 version
 * @param {Array} a items An array containing the items.
 */
function shuffle(a) {
    for (let i = a.length - 1; i > 0; i--) {
        const j = Math.floor(Math.random() * (i + 1));
        [a[i], a[j]] = [a[j], a[i]];
    }
    return a;
}

Note however, that swapping variables with destructuring assignment causes significant performance loss, as of October 2017.

Use

var myArray = ['1','2','3','4','5','6','7','8','9'];
shuffle(myArray);

Implementing prototype

Using Object.defineProperty (method taken from this SO answer) we can also implement this function as a prototype method for arrays, without having it show up in loops such as for (i in arr). The following will allow you to call arr.shuffle() to shuffle the array arr:

Object.defineProperty(Array.prototype, 'shuffle', {
    value: function() {
        for (let i = this.length - 1; i > 0; i--) {
            const j = Math.floor(Math.random() * (i + 1));
            [this[i], this[j]] = [this[j], this[i]];
        }
        return this;
    }
});