I don't know the exact time period but it was a couple of years back and I was looking for a fax cover letter at the time: http://faxcoversheet.info/
Interesting question. I still have a couple of clients who like to receive documents by fax. The last time I sent one was about 6 months ago. I think even these last holdouts will give it up soon, though, as there is no real advantage to it at this point.
I received a fax just 3 weeks ago and have sent one in the past week, but that was the first one I've received in nearly 3 years. Most companies are utilizing PDFs and sending them via email. However, in the US at least, the medical profession still utilizes fax for communication.
I have not sent or received a fax in the 21st century. My last send was circa 1998 for a job application and my last receive was at work in 1995.
If online faxing counts, I used it a week ago to apply for a job. I hadn't realized some employers still require that you either mail or fax them applications, so I used http://findafax.com/ to find a service to fax for free. Figured it was better and cheaper to fax my application than send it via snail mail.
Just used it a week ago to fax a signed contract for a media buy. It is limited but still requested.
That must have been in a time where the animals still talked... 8-)