How can I make custom UI controls for the QuickTime Player in HTML pages? (like Apple does on its site)
You need to use the QuickTime JavaScript API.
Make sure to check the section "Controlling QuickTime Using JavaScript", for some code examples.
You would be able to do the following:
<div>
<script language="javascript" type="text/javascript">
QT_WriteOBJECT('MyMovie.mov', '180','160', '',
'obj#id', 'movie1', 'emb#name', 'movie1', 'enablejavascript', 'true');
</script>
</div>
<p>Play and Stop Movie: <br>
<a href="javascript:document.movie1.Play();">Play Movie</a><br>
<a href="javascript:document.movie1.Stop();">Stop Movie</a><br>
</p>