Using jQuery is there a way to find the farthest (deepest, or most nested) child element?

Here's an implementation that uses a treeWalk function I had written earlier and then wraps it in a jquery method that finds the deepest descendant of each item in the passed in jQuery object and returns a new jQuery object containing those nodes.

A solution with recursion and lots of jQuery can be done with lots less code, but it will likely be slower. This is based on a generic native JS tree walk function that walks a tree.

Working demo with more complicated HTML test case than the OP's HTML: http://jsfiddle.net/jfriend00/8tC3a/

$.fn.findDeepest = function() {
    var results = [];
    this.each(function() {
        var deepLevel = 0;
        var deepNode = this;
        treeWalkFast(this, function(node, level) {
            if (level > deepLevel) {
                deepLevel = level;
                deepNode = node;
            }
        });
        results.push(deepNode);
    });
    return this.pushStack(results);
};

var treeWalkFast = (function() {
    // create closure for constants
    var skipTags = {"SCRIPT": true, "IFRAME": true, "OBJECT": true, "EMBED": true};
    return function(parent, fn, allNodes) {
        var node = parent.firstChild, nextNode;
        var level = 1;
        while (node && node != parent) {
            if (allNodes || node.nodeType === 1) {
                if (fn(node, level) === false) {
                    return(false);
                }
            }
            // if it's an element &&
            //    has children &&
            //    has a tagname && is not in the skipTags list
            //  then, we can enumerate children
            if (node.nodeType === 1 && node.firstChild && !(node.tagName && skipTags[node.tagName])) {                
                node = node.firstChild;
                ++level;
            } else if (node.nextSibling) {
                node = node.nextSibling;
            } else {
                // no child and no nextsibling
                // find parent that has a nextSibling
                --level;
                while ((node = node.parentNode) != parent) {
                    if (node.nextSibling) {
                        node = node.nextSibling;
                        break;
                    }
                    --level;
                }
            }
        }
    }
})();

var deeps = $(".start").findDeepest();

deeps.each(function(i,v){
    $("#results").append(
        $("<li>").html($(v).prop("tagName") + " " + $(v).html())
    );
});