clearTimeout(id_of_settimeout)

<ul class="header-nav">
<li class="nav-item home"><a href="@Url.Action("Index", "Home")">首页</a></li>
<li class="nav-item products" id="header_tags">
<a href="#">产品<span class="icon-caret-down"></span></a>
....
</li>
</ul>
<div class="header-tags">
<ul>
<li>
<img class="screening-img-normal" src="~/Content/static/all.png">
<img class="screening-img-hover" src="~/Content/static/all1.png">
<p>全部</p>
</li>
<li tagid="4">
<img class="screening-img-normal" src="~/Content/static/shafa.png">
<img class="screening-img-hover" src="~/Content/static/shafa1.png">
<p>沙发</p>
</li>
<li tagid="3">
<img class="screening-img-normal" src="~/Content/static/zuoyi.png">
<img class="screening-img-hover" src="~/Content/static/zuoyi1.png">
<p>座椅</p>
</li>
....
</div> 

/*父子*/
#a:hover #b{display: block} 
/*兄弟*/
#a:hover + #b{display: block} 

$(function () {
var tagsTime;
$(document).on('mouseover mouseout', '#header_tags', function(event){
var $headerTagsBox = $('.header-tags');
if (event.type == 'mouseover') {
clearTimeout(tagsTime);
$headerTagsBox.slideDown(300);
}
else if (event.type == 'mouseout') {
tagsTime = setTimeout(function(){
$headerTagsBox.slideUp(200);
}, 200);
}
});
$('.header-tags').hover(function(){
clearTimeout(tagsTime);
},function(){
var $me = $(this);
tagsTime = setTimeout(function(){
$me.slideUp(200);
}, 200);
}); });