Russ Cam is missing an edge case -- you can drag and drop text into and within input fields by highlighting and dragging, which his code does not account for.  
Below code that covers this case:
$(function() {
  var areaText = $('#area').val();  
  $('#text').bind('keyup keypress drop', dropfunction() { 
      $('#area')[0].value = areaText + $(this)[0].value;
  });
});
That said, there is still another edge case, which is deleting and manipulating via context menu.  As of right now I can't see a way to detect the selection of context menu interaction...  You could disable it if that is important using the following code
$('#text').bind('contextmenu', function() { 
    return false
});