My organization uses Better Impact that includes Emergency Contact fields. BUT I also keep a laminated spread sheet of volunteer's emergency contact information on my cubicle wall that any staff can access in a true emergency. We are small enough (under 100 volunteers) and localized to one building where this is an option. 

We are in the midst of this conversation as well.  We are up in the woods at Audubon, and have frequent power outages.  I am just beginning to print out who is on campus each week, so that in case of emergency we have paper copies of contact information.  

We bought Better Impact this year, and a LOVE it.  It's easy to access emergency contacts for volunteers as long as you have internet access.