Drag ‘n’ Drops For Lists – HTML5 Sortable
The drag 'n'drop interactions of jQuery UI (draggable, droppable and sortable) are probably the most popular solutions out there.
However, if you don't want to use jQuery UI just for this and would like to go with only a jQuery plugin, here it is: HTML5 Sortable.
This plugin uses the native HTML5 drag and drop API for creating sortable lists/grids and provides a similar API + behavior when compared to jQuery UI's sortable.
It is lightweight (<1kb when minified/gzipped), supports "connected lists (moving items between different lists)" and works in all major browsers.