• This is the title of a discussion about self-reference
    At the risk of my missing the point here, self-reference in a programming context is definitely handy. On the subjective side, several computing problems (e.g. path-finding, tree-traversal, searching) are more concisely and/or clearly written in a recursive fashion*. More concretely though, self-reference is essential for making radiation-hardened quines.

    Regular quines are fixed points of a programming language; programs which when executed can print their source code without reflection (i.e. without needing to be able to read their source code from the hard-disk).

    Radiation hardened quines are similar, but are also robust to the removal of one character. This is a useful property in environments where bits can be flipped/damaged on a regular basis (e.g. code on satellites - which are not shielded by the atmosphere); the program can repair itself.

    * Here's an example comparing an iterative vs. recursive implementation of the factorial function:
    # Iterative
    iterative_factorial( x ):
      x_factorial = 1
      while x > 1:
          x_factorial *= x
          x -= 1
      return x_factorial
    
    # Recursive
    recursive_factorial( x ):
      return 1 if x == 0 else (x * recursive_factorial(x-1))
    
    Full disclosure, the iterative function could be written more compactly than it is above depending on the language - but using just regular language features, the recursive solution is more easily made concise.

    As another example, writing a method to navigate a maze is naturally suited to recursion.
    You could write this algorithm in an iterative form, but the recursive way below seems more intuitive to me.

    # This function prints the path to the exit, if there is one.
    navigate( maze, path_taken ):
    
      current_position = get_position(maze, path_taken)
      past_positions = [get_position(maze, path_taken[:n]) for n in len(path_taken)]
      if current_position not in past_positions:
    
        if AT_EXIT: 
         print( path_taken )
         exit_program()
    
        else:
         if CAN_GO_STRAIGHT:
             navigate(maze, path_taken + [ STRAIGHT ])
         if CAN_GO_LEFT: 
             navigate(maze, path_taken + [ LEFT ])
         if CAN_GO_RIGHT: 
            navigate(maze, path_taken + [ RIGHT ])