Ruby 1.9+, 51 (or 58 or 60)
-

 a=*$<
 ?a.upto(?z){|c|$><<c*a.map{|l|l.count c}.max}

Assumes everything's in lowercase. Case insensitivity costs 8 characters via `.upcase`, while case insensitivity *and lowercase output* costs 9 characters via `.downcase`.