This code will work in all versions of Mozilla and IE.
function preventDrag(event)
{
 if(event.type=='dragenter' || event.type=='dragover' || //if drag over event -- allows for drop event to be captured, in case default for this is to not allow drag over target
    event.type=='drop') //prevent text dragging -- IE and new Mozilla (like Firefox 3.5+)
 {
  if(event.stopPropagation) //(Mozilla)
  {
   event.preventDefault();
   event.stopPropagation(); //prevent drag operation from bubbling up and causing text to be modified on old Mozilla (before Firefox 3.5, which doesn't have drop event -- this avoids having to capture old dragdrop event)
  }
  return false; //(IE)
 }
}
//attach event listeners after page has loaded
window.onload=function()
{
 var myTextInput = document.getElementById('textInput'); //target any DOM element here
 if(myTextInput.addEventListener) //(Mozilla)
 {
  myTextInput.addEventListener('dragenter', handleEvents, true); //precursor for drop event
  myTextInput.addEventListener('dragover', handleEvents, true); //precursor for drop event
  myTextInput.addEventListener('drop', preventDrag, true);
 }
 else if (myTextInput.attachEvent) //(IE)
 {
  myTextInput.attachEvent('ondragenter', preventDrag);
  myTextInput.attachEvent('ondragover', preventDrag);
  myTextInput.attachEvent('ondrop', preventDrag);
 }
}