...
One contender is YUI Calendar http://developer.yahoo.com/yui/calendar/ which has a BSD license.
...
The Interval Selection calendar is quite impressive. http://developer.yahoo.com/yui/examples/calendar/intervalcal.html
There appears to be no time support.
...
Another contender is jQuery DatePicker http://jqueryui.com/demos/datepicker/ which has a MIT and LGPL license.
...
This widget unfortunately has quite large dependencies 155.58 kb, minimised
There appears to be no time support.
CalendarDateSelect
Another option is CalendarDateSelect http://electronicholas.com/calendar which has a MIT license.
This control has time support, but has a JS dependency on the prototype library which could potentially impact JS code using the jquery library.