Floating Div Over An Image

Change your positioning a bit:

.container {
    border: 1px solid #DDDDDD;
    width: 200px;
    height: 200px;
    position:relative;
}
.tag {
    float: left;
    position: absolute;
    left: 0px;
    top: 0px;
    background-color: green;
}

jsFiddle example

You need to set relative positioning on the container and then absolute on the inner tag div. The inner tag's absolute positioning will be with respect to the outer relatively positioned div. You don't even need the z-index rule on the tag div.

Never fails, once I post the question to SO, I get some enlightening "aha" moment and figure it out. The solution:

    .container {
       border: 1px solid #DDDDDD;
       width: 200px;
       height: 200px;
       position: relative;
    }
    .tag {
       float: left;
       position: absolute;
       left: 0px;
       top: 0px;
       z-index: 1000;
       background-color: #92AD40;
       padding: 5px;
       color: #FFFFFF;
       font-weight: bold;
    }

<div class="container">
       <div class="tag">Featured</div>
       <img src="http://www.placehold.it/200x200">
</div>

The key is the container has to be positioned relative and the tag positioned absolute.