You should use either event.preventDefault() or a false return value:
<a href="board.php?id={$id}" onclick="javascript:parent.$.fancybox.open({href : 'board.php?id={$id}', type: 'ajax'});event.preventDefault();">
or
<a href="board.php?id={$id}" onclick="javascript:parent.$.fancybox.open({href : 'board.php?id={$id}', type: 'ajax'});return false;">
Really, though, you shouldn't use inline event handlers like this. You should give your link an id or class and attach the handler to it like this:
<a href="board.php?id={$id}" id="myElement">something</a>
<script>
document.getElementById('myElement').onclick = function () {
parent.$.fancybox.open({href : 'board.php?id={$id}', type: 'ajax'});
event.preventDefault();
};
</script>
This will make it much easier to read and maintain down the road.
Here's a simple jsFiddle demo.