How should a date be written? [duplicate]

I have most often seen "Wednesday, June 5, 2010", when the day of the week is included.

Usually, though, the day of the week is not included in the date; hence:

June 5, 2010 (for general U.S. and Canada usage)

5 June 2010 (for general U.K. and related usage)

The preceding examples pertain mainly to non-technical usage. For technical or more rigorous usages, you should use a numeric format (e.g. 2010-06-05 or 06-05-2010). If you do use a numeric format, be sure that the numeric format is compatible with the situation you use it in; if you're not careful, you might accidentally switch MM with DD.

For further information, reference this question.

As @drm65 has pointed out, there are various international standards, and it's not common to include the day of the week. However, there is one important exception: formal event announcements. It's quite customary to include the day of the week in a wedding invitation, for instance. (I can only speak for American customs, of course; British invitations might be in binary for all I know.) Here are a few valid formats:

Spelling out all numbers - quite formal, and a little unnatural:
Wednesday, the fifth of June, two thousand ten, at four o'clock in the afternoon.

All numbers in digits - much less formal; maybe too informal to be quite natural:
Wednesday June 5, 2010 at 4 p.m.

Compromise: Wednesday, June fifth, 2010, at four o'clock in the afternoon

There are other possibilities, of course. In general, you can use "June 5th", "June fifth", or "the fifth of June"; "the 5th of June" and "June the fifth" look a little strange; don't use "fifth June".

I personally like and use "5 June 2010" (back when I used to write actual paper checks, that was my preferred format), but I wouldn't put it on an invitation.