How widespread are electronic-only dissertations? My university currently archives all our graduate dissertations as bound volumes in the library.  We are considering dropping this practice and archiving them electronically only.

How common is this practice among respected research universities?  Is there any data?

(Some of my colleagues feel that having paper dissertations on the shelves is an important mark of a serious research university, and that dropping them will harm our institutional reputation.  So it would be helpful to have data to indicate whether such a policy would be "mainstream" or "fringe".)
The first page of a Google search shows UVA and USC do this already.  You could try contacting colleagues at those schools and see how the experience has been.  (Sorry, I don't have a statistic.)

P.s. I am sympathetic to those who prefer the bound volumes.  I think you can in some ways scan a text and multiple texts more easily in the hard copy than electronic.  Also, there are excellent arguments that books on acid free paper are a superior storage media than computer files (longer lasting, safer, future readable).  Finally I think that the granting university is more likely to have future students working in the same general area.  Thus they benefit especially from a printout.