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;
}