I'm American, so I'm in the Month/Day/Year group. As with other things, such as the metric system, our date system is not as logical as the other ones, but it's so deeply-ingrained at this point that it would be tough to remove it from our collective psyche.
However, I can somewhat see the reasoning behind the Month/Day/Year format: order of importance, rather than chronology or other things. Think of an event. What is one of the first things you remember about it? How you felt, right? What's related to how you felt? Temperature/weather. Now, here's the thing. Temperature and weather vary more on a monthly basis than they do on a daily or yearly basis. Unless the weather goes from bright and sunny to hurricane the next day, the weather each day is pretty similar each day, and August 2nd might not seem so different from the 3rd or the 10th. Now compare August to other months. Comparing it to September would yield differences (unless you're in the tropics, where monthly climate doesn't change much). Compare August and September in Baltimore and you're going to have hot and cool months. Now compare 2010 to 2009, weather-wise? Not much difference, is there? So, when tracking a memory, you're most likely to recall the month before the day, and the year is typically already a given, so it's more of an afterthought.
Now, truly, that would make Year/Month/Day a more logical system, since it's from most-certain to least-certain. It is also much better to work with in computer systems than either Day/Month/Year or Month/Day/Year. (This makes cases where the year is static much easier to work with in the American system of Month/Day than the other system of Day/Month.)
