Azexo Composer uses client JS for render of HTML to work faster and save server resources.
GridList is a drag and drop library for two-dimensional, resizable and responsive lists.
Draggabilly is a separate library that makes elements draggable. It supports IE8+ and multi-touch.
interact.js is a powerful, flexible, snappable drag and drop, resizing and multi-touch gestures for modern browsers (and also IE8+)
fieldChooser is a jQuery plugin for selecting from a list of fields or values (the source) and adding them to a new list (the destination).
You move fields from the source to the destination by dragging and dropping with multi-select. Fields themselves can be simple HTML elements or more complex containers.
ElastiStack is a little script that let's you navigate through a stack of items by dragging away the first one.
It comes with an elastic touch meaning that when dragging the top-most item, the other ones will follow as if they were connected elastically. When reaching a certain distance, the dragged item will release itself and the next item will pop out.
Images: crop, resize and auto orientation by EXIF.
Gridly is a jQuery plugin to enable dragging and dropping as well as resizing on a grids.
Dynatree is a dynamic tree view plugin for jQuery with support for persistence, keyboard, checkboxes, drag'n'drop, and lazy loading.
Nice tutorial about creating an AJAX file upload form, that will let visitors upload files from their browsers with drag/drop or by selecting them individually.