Some places I find myself using corecursion:

Minimax algorithm: https://en.wikipedia.org/wiki/Minimax (I actually generally use negamax, the non-corecursive version, but you should understand minimax first)

"Tying the knot" in Haskell

That is, it's possible to create circular lists in Haskell like so:

    let x = 1:y    -- x = 1 cons y
        y = 0:x    -- y = 0 cons x
    in x           -- return x

Which will return an infinite list of alternating 1's and 0's which only take up 2 ints (and pointers) worth of memory. Calling the millionth index merely runs in circles around the list until it's followed a million pointers.

EDIT: Minimax is mutual recursion, not corecursion, whoops.