When are binary trees better than hashtables in real world applications?
Hash tables can only tell you if an element is present or not. 

Here are somethings you can do with a binary tree that you can't do wiht a hash table.


sorted traversal of the tree
find the next closest element
find all elements less than or greater than a certain value


See this wikipedia article on K-d trees for an example of a real world data structure that makes use of the special properties of binary trees.
http://en.wikipedia.org/wiki/K-d_tree