Grammar Pulis

You ask: I know both forms are correct, but when is it proper to write the date this way: April 2, 2009 and this way: 2 April 2009?

Grammar Pulis Answers: Yes, both forms are correct. And the way you punctuate those dates is also correct. If you use the month-day-year format, you should insert a comma in between the day and the year. If you choose the day-month-year format, then omit the comma.

Both examples here are correct then:
April 2, 2009
2 April 2009

It's also good that you spelled out the month.

Can you imagine the confusion if the dates are written these ways?
2/4/2009
or 4/2/2009

As to when you should use them, my default answer based on my stock knowledge would have been to:

• use the month-day-year format, the traditionally considered US format, when you're corresponding with somebody from the USA, or a country that predominantly follows Standard American English, and
  
• use the day-month-year format if you're corresponding with Europeans and countries that lean toward British English .
  

Wikipedia also makes this distinction.

However, I decided not to rely on stock knowledge and checked other sources. Several sources were silent on the matter, but the Chicago Manual of Style and Strunk and White's The Elements of Style agree that both formats are acceptable in the US. So, you can use either. Just try to be consistent if you're going to mention many dates in a document. Choose one style and stick to it.

It then becomes a matter of personal preference. Unless the organization, industry, or community you write for prescribes a specific style, you can chose the format that you're most comfortable with. Some organizations, for example, require dates to be formatted according to ISO standards.

Strunk and White prefers the day-month-year format, 22 April 2009. The word separating the figures contributes to clarity. Eliminating the comma also very subtly reduces clutter. I think those are 2 great reasons to choose 2 April 2009.