Do people still ask that question?
Arguably it is redundant as establishing why you should hire someone is surely the reason for the interview in the first place. As a question I would say it is to direct, and will only show how much someone has prepared, and how well they can deliver a planned answer.
Its much better to ask less direct questions that will reveal information without the applicant realising what you want to hear. Most of us have sat through an interview and been told exactly what they think we want to hear and as a result learnt very little.
I would much prefer to see the question "Why shouldn't we hire you?" This will at least show if someone is arrogant, or if they are able to recognise their own shortcomings.
If I was ever asked, I hope I would answer with something along the lines of "I believe I have already answered that. If over the last half an hour you haven't been able to figure out the answer that's a shame, but thank you for your time". Of course I may just cave and reel off a list of semi true qualities.