Use a date format like this:
SimpleDateFormat sdf = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSSX");
to match the input string format.
For details, consult the documentation.
For example this
public static void main(String[] args) throws ParseException {
String dateStr = "2014-01-01T21:13:00.000Z";
SimpleDateFormat sdf = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSSX");
Date birthDate = sdf.parse(dateStr);
System.out.println(birthDate);
}
prints (actual output depends on your time zone)
Wed Jan 01 22:13:00 CET 2014