As a button value is an attribute you need to use the .attr() method in jquery. This should do it
<script type="text/javascript">
$(document).ready(function() {
$('.my_button').click(function() {
alert($(this).attr("value"));
});
});
</script>
You can also use attr to set attributes, more info in the docs.
This only works in JQuery 1.6+. See postpostmodern’s answer for older versions.