in reply to How To: Make An Iterator
Maybe this is too obvious to be worth mentioning, but under "Why Are Iterators Useful" I would add that they offer a uniform interface for traversal. The underlying data structure may change (and with it the traversal algorithm), but the iterator interface remains constant.
A corollary benefit is that iterators reify the process of traversal, so that one can begin to think of functions that take among their arguments both a data structure and an iterator. For example, one could implement a generalization of map that took three arguments: a data structure, an iterator for the data structure, and some function to be applied to each element of the data structure; and returned the list resulting from applying the function to each element of the data structure in the order prescribed by the iterator.
Update: Added second paragraph.
the lowliest monk