Finding DOM node index

The shortest possible way, without any frameworks, in all versions of Safari, FireFox, Chrome and IE >= 9:

var i = Array.prototype.indexOf.call(e.childNodes, someChildEl);

A little shorter, expects the element to be in elem, returns k.

for (var k=0,e=elem; e = e.previousSibling; ++k);

After a comment from Justin Dearing I reviewed my answer and added the following:

Or if you prefer "while":

var k=0, e=elem;
while (e = e.previousSibling) { ++k;}

The original question was how to find the index of an existing DOM element. Both of my examples above in this answer expects elem to be an DOM element and that the element still exists in the DOM. They will fail if you give them an null object or an object that don't have previousSibling. A more fool-proof way would be something like this:

var k=-1, e=elem;
while (e) {
    if ( "previousSibling" in e ) {
        e = e.previousSibling;
        k = k + 1;
    } else {
        k= -1;
        break;
    }
}   

If e is null or if previousSibling is missing in one of the objects, k is -1.

RoBorg's answer works... or you could try...

var k = 0;
while(elem.previousSibling){
    k++;
    elem = elem.previousSibling;
}
alert('I am at index: ' + k);

A modern native approach might include Array.from(e.children).indexOf(theChild)

No IE support, but Edge works: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/from