To me the most logical system is the one the Japanese and other countries use - Year, month, day. E.g. 2012-06-01. Why? Because if you are saving or cataloguing files in numerical order, particularly on a computer system, this system ensures everything is kept in date order, from most recent to most long ago (or reverse, if you reverse the order).
I have to admit, I initially clicked on this thread because I thought it would be about systems used in dating. i.e. going out with people!!