It is possible to make a link fill the entire div which gives the appearance of making the div clickable.
CSS:
#my-div {
background-color: #f00;
width: 200px;
height: 200px;
}
a.fill-div {
display: block;
height: 100%;
width: 100%;
text-decoration: none;
}
HTML:
<div id="my-div">
<a href="#" class="fill-div"></a>
</div>