1.1.0 - Fixed a bug where it would grab all custom apps and not just the ones for this view

ZendeskOrderApps.user.js

// ==UserScript==
// @name Zendesk - Set App Order
// @namespace com.opendns.zendesksetapporder
// @author Brian Hartvigsen <bhartvigsen@opendns.com>
// @version 1.1.0
// @description Allow you to reorder your Apps to get the most important ones on top
// @match https://*.zendesk.com/agent/*
// @include https://*.zendesk.com/agent/*
// ==/UserScript==

function orderApps() {
    order = [
        'app-10954', // Answer Suggestion
        'app-6848', // Five Most Recent
        'app-10', // Salesforce
        'app-5796' // Quick Search
    ];

    jQuery.getScript("https://mutation-summary.googlecode.com/git/mutation_summary.js", function() {
        var ms = null;

        function handleChanges(changes) {
            // ignore removals/deletions
            if (changes[0].added.length <= 0) {
                return;
            }

            // We are about to mess with the dom, so let's not listen to changes
            ms.disconnect();

            // Start at the end, instert it at the top of the list
            // then loop through all the elements
            _.each(order.slice(0).reverse(), function(appid){
                var elem = jQuery("div.workspace:visible div.ember-view.app_view." + appid);
                elem.insertAfter(elem.parent().find(".action_buttons"));
            });

            // and back to listening to changes
            ms.reconnect();
        }

        jQuery(function(){
            ms = new MutationSummary({
                callback: handleChanges,
                queries: [
                    { element: "div.ember-view.custom.app_view" }
                ]
            });

            handleChanges([{added: [ true ]}]);
        });
    });
}


function addScript(js) {
    var body = document.body, script = document.createElement('script');
    if (!body) return;
    script.type = 'text/javascript';
    script.textContent = "(" + js + ")()";
    body.appendChild(script);
}

addScript(orderApps);