Based on the number of applications and the number of enrollees in the 2006-2007 Official Guide to Dental Schools, I figured out this much:
This is an estimate as it is based on data from two different years but is better than no info...
Entering class of 2004-2005 had 9433 applicants and 4612 enrolled.
74062 applications were filled out for the entering class of 2005-2006.
Based on these two numbers we can approximate an average of 8 schools applied to with an acceptance rate of 47% overall. Pretty competetive!