Use event delegation by assigning the onclick to the <ol>. Then pass the event object as the argument, and using that, grab the text from the clicked element.
function addText(event) {
var targ = event.target || event.srcElement;
document.getElementById("alltext").value += targ.textContent || targ.innerText;
}
<textarea id="alltext"></textarea>
<ol onclick="addText(event)">
<li>Hello</li>
<li>World</li>
<li>Earthlings</li>
</ol>
Note that this method of passing the event object works in older IE as well as W3 compliant systems.