How to get a word under cursor using JavaScript?

My other answer works only in Firefox. This answer works in Chrome. (Might work in Firefox, too, I don't know.)

function getWordAtPoint(elem, x, y) {
  if(elem.nodeType == elem.TEXT_NODE) {
    var range = elem.ownerDocument.createRange();
    range.selectNodeContents(elem);
    var currentPos = 0;
    var endPos = range.endOffset;
    while(currentPos+1 < endPos) {
      range.setStart(elem, currentPos);
      range.setEnd(elem, currentPos+1);
      if(range.getBoundingClientRect().left <= x && range.getBoundingClientRect().right  >= x &&
         range.getBoundingClientRect().top  <= y && range.getBoundingClientRect().bottom >= y) {
        range.expand("word");
        var ret = range.toString();
        range.detach();
        return(ret);
      }
      currentPos += 1;
    }
  } else {
    for(var i = 0; i < elem.childNodes.length; i++) {
      var range = elem.childNodes[i].ownerDocument.createRange();
      range.selectNodeContents(elem.childNodes[i]);
      if(range.getBoundingClientRect().left <= x && range.getBoundingClientRect().right  >= x &&
         range.getBoundingClientRect().top  <= y && range.getBoundingClientRect().bottom >= y) {
        range.detach();
        return(getWordAtPoint(elem.childNodes[i], x, y));
      } else {
        range.detach();
      }
    }
  }
  return(null);
}    

In your mousemove handler, call getWordAtPoint(e.target, e.x, e.y);

Further to the two other answers, you may be able to split your paragraphs up into spans using jQuery (or javascript generally).

That way, you wouldn't need to think about outputting your text with spans around the words. Let your javascript do it for you.

e.g.

<p>Each word will be wrapped in a span.</p>
<p>A second paragraph here.</p>
Word: <span id="word"></span>

<script type="text/javascript">
    $(function() {
        // wrap words in spans
        $('p').each(function() {
            var $this = $(this);
            $this.html($this.text().replace(/\b(\w+)\b/g, "<span>$1</span>"));
        });

        // bind to each span
        $('p span').hover(
            function() { $('#word').text($(this).css('background-color','#ffff66').text()); },
            function() { $('#word').text(''); $(this).css('background-color',''); }
        );
    });
</script>

Note that the above code, while it works, will strip out any html inside your paragraph tags.

jsFiddle example