Native javascript equivalent to jQuery.draggable()

There is the HTML5 dnd api, but since nobody i've talked to liked it in any way and none of the older browsers support it,I would say you found a good solution in jQuery.

Use the HTML5 methods which seem cleaner than jQuery's:

<div draggable="true"
  ondragstart="event.dataTransfer.setData('text/plain', '12345')">
drag me
</div>

<div ondragover="return false;" 
  ondrop="this.innerHTML=event.dataTransfer.getData('text/plain')">
drop on me
</div>

Although the question states native JavaScript, I'm going to respond given that @Moe Sweet commented that jQuery was enabled.

Drag and drop is a particular event chain. It's not obscenely difficult, but it can be challenging.

Simply put, drag and drop is the following steps/events:

1. Mouse pressed down, dragging is enabled
2. Mouse is moved, dragging continues
3. Mouse is let up, dragging is disabled

The simple solution is to use those events: mousedown, mousemove, and mouseup

$(anElement).mousedown(foodown);

function foodown(){
  $(window).mousemove(foomove).mouseup(fooup);
  //stuff
}

function foomove(){
  //stuff
}

function fooup(){
  //stuff
  $(window).unbind('mousemove', foomove).unbind('mouseup', fooup);
}

A point that should be noticed is that the events following the mousedown need to be bound to the window so that they are caught if the mouse has left the original element while being held down.

The "stuff" part of the code is where you'll need to check the screen coords of the element vs the screen coords of the mouse and move things appropriately. Motion is only really necessary during the mousemove event as the mouse wont have moved for a mouseup or mousedown event.

There is a similar question where I posted my code for a jQuery.dragondrop plugin.