UPDATE

I've written a simpler version of this that also works in IE < 9:

https://stackoverflow.com/a/4812022/96100

Old Answer

This is actually a more useful result than a character offset within the text of the whole document: the startOffset property of a DOM Range (which is what window.getSelection().getRangeAt() returns) is an offset relative to its startContainer property (which isn't necessarily always a text node, by the way). However, if you really want a character offset, here's a function that will do it.

Here's a live example: http://jsfiddle.net/timdown/2YcaX/

Here's the function:

function getCharacterOffsetWithin(range, node) {    var treeWalker = document.createTreeWalker(        node,        NodeFilter.SHOW_TEXT,        function(node) {            var nodeRange = document.createRange();            nodeRange.selectNode(node);            return nodeRange.compareBoundaryPoints(Range.END_TO_END, range) < 1 ?                NodeFilter.FILTER_ACCEPT : NodeFilter.FILTER_REJECT;        },        false    );    var charCount = 0;    while (treeWalker.nextNode()) {        charCount += treeWalker.currentNode.length;    }    if (range.startContainer.nodeType == 3) {        charCount += range.startOffset;    }    return charCount;}

This is a very old post, but still one of the first results searching on Google, so maybe still useful. This works for me to get right position considering html tags and newlines as well (tested on Firefox):

function getCaretPosition (node) {    var range = window.getSelection().getRangeAt(0),        preCaretRange = range.cloneRange(),        caretPosition,        tmp = document.createElement("div");    preCaretRange.selectNodeContents(node);    preCaretRange.setEnd(range.endContainer, range.endOffset);    tmp.appendChild(preCaretRange.cloneContents());    caretPosition = tmp.innerHTML.length;    return caretPosition;}

It uses the cloneContents functionality in order to get the actual html and appends the documentfragment to a temporary div in order to get the html length.

If you want to insert element then you could try to do something like this:

// Get rangevar range = document.caretRangeFromPoint(event.clientX, event.clientY);if (range)  range.insertNode(elementWhichYouWantToAddToContentEditable);