A friend of mine, a respected linguist, mentioned recently that "despite" (prep) is outdated. Whilst it is true that I hardly ever hear someone using the word in ordinary conversation, I still hear it in scientific seminars, lectures, congresses, etc and I also come across it in technical texts once in a while. What I mean here is "despite" and not "despite of" or "in despite of" which are clearly archaic. The search I've done includes the mainstream dictionaries (ODO, TFD, Merriam-Webster, etc) and they don't mention the word being outdated.
It's alive and well.
is it still being used?
An example, from the Associated Press, dated tomorrow
(so, it seems not only is it being used now, it will still be used in the future!)
American businesses ramped up hiring last month, in the latest sign that the nation’s economy is expanding despite worries about global growth.