Be cautious. Why are they so desperate? Is your place that amazing? Rental market that tight?
More common with short term or company relocations. Less common long term.
I recently did a Skype tour with a set of applicants who were moving from 7hrs away. Went very well and rented to them. Use technology to your advantage.
The only "sight unseen" rentals I do are for my short-term super-suite. For a 2 - 6 month lease, I can tolerate anyone and the tenant can be expected to tolerate the suite even if it isn't exactly what he hoped for.
Otherwise, I won't do them. I have tried a couple of times with no success. In one case the tenant had higher expectations about the neighbourhood (which is difficult to showcase on a video tour).
Furthermore I have found a personal meeting with prospective tenants is much more revealing than any phone or video chat. Sometimes you (or your manager) can't possibly get a true sense of one's personality until you meet in person. Then suddenly you may see the person is not suitable (or the truth behind lies is revealed).