What is the best format to use when writing out dates?

The context that matters most is where you are located geographically (or which variety of English you otherwise wish to employ).

Paul covered the case of the US: "April 1, 2010". That would surely be understood in the UK too, but to my knowledge "1 April 2010" (NB: no comma) or "1/4/2010" would be more common there.

Edit: Based on some quick "research" I just did, most commonwealth countries (Australia, New Zealand, South Africa) also seem to prefer "1 April 2010", while in Canada "April 1, 2010" would be more common (probably due to US influence).

As Paul mentioned, YYYY-MM-DD is pretty good for getting across universally, yet concisely. In my opinion the format often used by airlines – "01 Apr 2010" – is useful too; there isn't much room for misinterpretation there.

In the United States, it is customary to write "April 1, 2010", regardless of context. This is spoken, however, as "April first, 2010".

I would discourage using MM/DD/YYYY (e.g. 4/1/2010) format, because this may cause confusion as the rest of the world writes the day before the month. If you really need to write dates in a consise format, I recommend YYYY-MM-DD format.

There's now an international standard of date format, aka ISO8601 - so if you care about making the world a better and less confusing place, you should only use the standard - YYYY-MM-DD, forever dropping the old local date format ideas.

I always write the month as either "Apr" or "April" and the year like 2010 to avoid any confusions. For example,

01/04/10

is way too ambiguous.

1 Apr 2010

is much clearer. Personally I prefer

2010-04-01

but I realize that this is because I am a geek, i.e. the chances of this format being accepted generally are pretty slim.