In programming, recursion is really a special case of iteration - one where you use the call stack as a special means of storing state. You can rewrite any recursive method to be an iterative one. It may be more complicated or less elegant, but it's equivalent.
In mathematics, there are certain problems that require recursive techniques to arrive at an answer - some examples are finding roots (Newton's Method), computing primes, graph optimization, etc. However, even here, there's just a question of how you differentiate between the terms "iteration" and "recursion".
EDIT: As others have pointed out, there exist many functions whose definition is recursive - ex. the Ackermann function. However, this does not mean that they cannot be computed using iterative constructs - so long as you have a turing complete operation set and unlimited memory.
