What's the recommended way to refer to the September 11 attacks in formal writing?

I think your question uses the most readily understood and formal way of referring to the events of that day: September 11 Attacks. Indeed, that's the name of the Wikipedia page.

9/11 (nine-eleven) is the informal "shorthand" that usually comes from people wanting to either exploit the event to push an agenda or bring out a more emotional response. Personally, I'd avoid using it in formal writing.

If you are writing for posterity (as opposed to writing for a periodical or something of similar, limited currency) I would introduce the event as "the attacks of September 11, 2001". We are nearly a decade out now, and people have a horrible habit of memorializing one such event with another, similar one. That leaves aside consideration of mere coincidence -- Ireland now has two Bloody Sundays, so when discussing the particulars of one or the other, you need to distinguish which one you are talking about. (Both carry the same emotional resonance if they're just mentioned in passing.)

Also please take in account that "9/11" can be misleading to most of the world. There are already a lot of people, who think that the attacks have occurred on 9th of November.

The issue is, that USA is almost the only country in the world, which uses MM/DD/YYYY date format.

See: http://en.wikipedia.org/wiki/Date_format_by_country