you can call javascript method on change event as below
<asp:listbox id="ListBox1" runat="server" onchange="PlayVideo(this);" >
<asp:listitem text="Video one" value="http://www.youtube.com/v/ylLzyHk54Z0"></asp:listitem>
<asp:listitem text="Video two" value="https://www.youtube.com/v/vGR5h2sqrXw"></asp:listitem>
<asp:listitem text="Video three" value="https://www.youtube.com/v/4xfTsO21RiM"></asp:listitem>
<asp:listitem>
</asp:listitem></asp:listbox>
and create method in javascript to play selected video
function PlayVideo(list) {
var videoID = list.value;
var params = { allowScriptAccess: "always" };
var atts = { id: "ytPlayer" };
swfobject.embedSWF(videoID + "&enablejsapi=1&playerapiid=player1", "videoDiv", "480", "295", "8", null, null, params, atts);
}
update :
<script type ="text/javascript" src="http://ajax.googleapis.com/ajax/libs/swfobject/2.2/swfobject.js"></script>
<script type ="text/javascript">
function PlayVideo(list) {
var flashvars = {};
var params = { wmode: 'opaque' };
var attributes = { name: "mymovie" };
swfobject.embedSWF(list.value + "&enablejsapi=1&playerapiid=player1", "videoDiv", "400", "200", "8.0.0", null, flashvars, params, attributes);
}
</script>