draggable.cmp

<aura:component implements="force:appHostable">
    <div>
        <div aura:id="draggable" draggable="true" class="draggable"></div>
        <div aura:id="draggable" draggable="true" class="draggable"></div>
    </div>
</aura:component>

draggable.css

.THIS .draggable{
    width: 200px;
    height: 100px;
    background-color: #F00;
    margin: 20px;
    cursor: move;
}

draggableApp.app

<aura:application >
	<c:draggable ></c:draggable>
</aura:application>

draggableRenderer.js

({
    afterRender: function(cmp, helper) {
        var draggables = cmp.find('draggable');
        draggables.forEach(function(draggable){
          var draggable = draggable.getElement();
            [
                'touchstart',
                'mousedown',
                'focus',
                'dragstart',
                'drag',
                'dragenter',
                'dragleave',
                'dragover',
                'drop',
                'dragend'
            ].forEach(function(eventName){
                $A.util.on(draggable, eventName, function(evt){
                    console.info(eventName, evt);
                    evt.stopImmediatePropagation();
                });
            });
        });
    }
})