Can every recursion be converted into iteration?

A reddit thread brought up an apparently interesting question:

Tail recursive functions can trivially be converted into iterative functions. Other ones, can be transformed by using an explicit stack. Can every recursion be transformed into iteration?

The (counter?)example in the post is the pair:

(define (num-ways x y)
  (case ((= x 0) 1)
        ((= y 0) 1)
        (num-ways2 x y) ))

(define (num-ways2 x y)
  (+ (num-ways (- x 1) y)
     (num-ways x (- y 1))