Okay, I have a burning question about BE usage on this admittedly minor point.
In the US, the standard written form "March 4" (still preferred) is pronounced "March fourth" (hence the corny pun on "forth"). Which is why "th" is (preferably) omitted in writing, the ordinal forms/suffixes being already understood. (So beware, for example, of Microsoft's supposed auto-correct, which not only wrongly adds "th" but even superscripts it. Boo, hiss, tacky.)
I was interested to learn from Ghol that "th" is also superfluous in the UK, I assume because it's spoken there too.
However, now that we sometimes see the BE written form "4 March" over here, for some reason Americans seem to have more trouble pronouncing it. So, my dumb question: do Brits read this out loud as "the fourth of March"? Or just "fourth of March"? Or "fourth March"? (To my ear the last two grate, much like, say, "in US" instead of "in the US".)
And finally, is it ever okay to say "four" instead of "fourth" in a date? I would hope not, but I feel like I've heard a few sort of wannabe-cool US media types saying "four March" (or even "March four," which I know is wrong).
PS: On my way out I'll side with Kevin and offer my $.02 against using the form 1970-03-04 (which BTW I might easily read as April 3) within any written English text. To me that looks like programming language, not English, and should be reserved for purely numerical contexts such as databases.