UPDATE
I have reverted back to Jquery 1.3.2 and everything is working, not sure what the problem is/was as I have not changed anything else apart of t
Seems to happen with some themes (cupertino/theme.css) in my case.
And the problem is the .ui-helper-hidden-accessible class which have clip property, like previous users said.
Just Overwrite it and it will be fine
$(document).ready(function() {
$("#datePicker").datepicker({ dateFormat: "yy-m-d" });
$('#ui-datepicker-div').css('clip', 'auto');
});