调试易

没做个阻止事件冒泡，搜了一下，这样试试
在二级列表处加一句，这样：
<li onclick="showDiv(this,2,'up');window.event.cancelBubble = true;">

需要将event对象传递到showDiv中<li onclick="showDiv(event,this,2,'up');">
function showDiv(event,this,n,up){
    //......省略的代码
    if (event.stopPropagation){
        event.stopPropagation();
    }else {
        event.cancelBubble = true;
    }
}

原理就这样，浏览器兼容要自己搜一搜
试试：
<li onclick="showDiv(this,2,'up');if (event.stopPropagation){event.stopPropagation();else event.cancelBubble = true;">

<style>
    ul{ display:none;border: 1px solid red;margin-left:10px}
</style>
<ul id="nav_left" class="nav_left" style="display: block">
    <li><a href="#">一级标题</a>
        <ul>
            <li><a href="#">二级标题</a>
                <ul>
                    <li><a href="#">三级标题</a>
                        <ul>
                            <li><a href="#">四级</a>
                                <ul>
                                    <li><a href="#">N级标题</a></li>
                                </ul>
                            </li>
                        </ul>
                    </li>
                </ul>
            </li>
        </ul>
    </li>
    <ul>
<script type="text/javascript">
    $(document).ready(function(){
        /*
        $("li").click(function (e) {
            $(this).children("ul").slideDown(300);
            e.stopPropagation();//阻止冒泡
        });
        $("li").mouseleave(function(e){
            $(this).children("ul").slideUp(300);
        });
        */
        $("li").hover(function(){
            $(this).children("ul").slideDown(300);
        },function(){
            $(this).children("ul").slideUp(300);
        })
    })
</script>