<script>
function changeImage(id, url) {
var target = document.getElementById(id);
target.style.backgroundImage = "url(" + url +")";
}
</script>

<table>
<tr><td id="test1">#test1</td></tr>
<tr><td id="test2">#test2</td></tr>
</table>

<a href="javascript:changeImage('test1', 'http://www.google.co.kr/logos/2012/newyearsday-2012-res.jpg')">변경 test1</a>
<span style="cursor:pointer" onclick="changeImage('test2', 'http://www.google.co.kr/logos/2012/newyearsday-2012-res.jpg')">변경 test2</span>

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anchor 태그보다는 span 같은 것 쓰시고 pseudo javascript보다는 event를 쓰시는 것이 좋습니다용.

감사합니다!! ㅠㅠ

jquery 를 쓰시면
jQuery(document).ready(function(){
jQuery("#A").click(function(){
jQuery(this).css("background-image","url(B)");
});
});