I've always been under the impression that the only real useful.. use.. of constants is when you are creating a program that you want to be able to easily modify later, or you want to make it easy for others to modify it...
For example, if you make a program that uses a group name like 'Blah' in the program and says, 'Welcome to Blah'.. and it also uses the name many more times later in the program. Instead of using cout<<"Blah", you use cout<<const... then, you only have to modify the variable once before compiling to change all occurences of Blah to something else.