Three ways to denote a date

To denote an exact date, one must provide 3 bits of information - the year, which month, and the specific date. Those 3 bits can be arranged in different ways - there seems to be some disagreement which is more correct - it differs by country, company, system, and culture.

Option 1: Year Month Date

We state time in decreasing increments - from larger to smaller - hours, then minutes, and down to seconds. Maintaining continuity with that logic, the idea that drives this option is this - start with chaos and refine to specific. When referring to a date, it makes sense to state the year first - that narrows the chaos down to 1 of 365 days, then the month - now, we're down to one of 28-31 days, then the specific date. The reader or listener is taken from the broad to the specific in a logical easy-to-follow format. If the listener, reader, or audience knows the year referenced, one can omit the year and just give month and date (above right).
Sometimes, the year is not necessary as those involved in the exchange assume the year is the current one and the year could then be omitted from stating the date. Then, the logical system is adhered to but also respects the prevailing custom of month and date. If all numbers are used (1950-27-07), there can be some confusion when the date is 12 or less. Does 10-8-12 mean December 8, 2010, August 10, 2012, or October 8, 2012? This confusion can be minimized if the culture has agreed upon this particular system.
Another solution is to use letters for the month, full or abbreviated: YYYY MMM DD or YYYY Mmm DD, like 2012 APR 04 or 2012 April 4. This method is used in China, Japan, and Korea; by the US military and The New York Times:

This format is the one preferred and promoted by the the ISO (The International Organization for Standardization).
In 1946 October, delegates from 25 countries met in London to create the International Organization for Standardization; it began operations in 1947 February 23. The organization promotes worldwide proprietary, industrial and commercial standards. It is headquartered in Geneva Switzerland, and works in 164 countries to facilitate world trade by providing common standards among nations. Nearly 20,000 standards have been set covering manufactured products, technology, food safety, agriculture, and healthcare.

ISO 8601 Data elements and interchange formats - Representation of dates and times was issued by the ISO in 1988. This standard provides an unambiguous and well-defined method of representing dates and times, so as to avoid misinterpretation of numeric representations, particularly when data is transferred between countries with different conventions for writing numeric dates and times. When dates are represented with numbers they can be interpreted in different ways. This uncertainty can be very frustrating, in a business context it can be very expensive. Organizing meetings and deliveries, writing contracts and buying airplane tickets can be very difficult when the date is unclear.
Date and time values are ordered from the largest to smallest unit of time: year, month (or week), day, hour, minute, second, and fraction of second: YYYY-MM-DD
YYYY-MM-DD sorts both alphabetically and numerically.
Representations and formats of dates use the Gregorian calendar and times are based on the 24-hour timekeeping system.
Each date and time value has a fixed number of digits that must be padded with leading zeros. The first of the month is 01.
Representations can be done in one of two formats - basic, with no separators (19661230) or extended, with separators to enhance human readability. The basic format should be avoided in plain text. The separator used between date values is the hyphen, while the colon is used as the separator between time values. Example, 2009-01-06, 08:15.
ISO 8601 prescribes a four-digit year (YYYY) to avoid the year 2000 problem. It represents years from 0000 to 9999, year 0000 being equal to 1 BCE.

Option 2: Date Month Year

This option is driven by the concept of stating the most important info first - the date of the event/activity, then progressing sequentially to the month, then the year. As with YearMonthDate, if all numbers are used (10-8-12) there can be some confusion. This method is popular in Europe and in the flight info from United Airlines (above right).

Option 3: Month Date Year

This system - commonly used in the USA - is based on the notion that the year is usually understood; the only info needed is the month, then the date. If the year is needed, then it is tacked onto the end of the date, as supporting clarification. But, adding it to this end makes it less sequential and less logical.