I was hoping for a few concrete examples of where comonads can be useful. I have found the need for monads fairly often in my code but I've never found any reason to use a comonad.
I think the more striking example is the first: "builders" with a default starting value form a comonad, which is the dual of the Writer monad. A Haskell implementation can be found in package 'comonad-transformers' as the 'Traced' comonad.
Infinite streams also form a comonad ('Data.Stream.Infinite' from the 'streams' package).
Inductive data types are defined by how they are constructed, while coinductive types are defined by how they are deconstructed (or observed). It's object instantiation vs field destructuring/patten matching. Turns out that OOP and protocols give you uniform deconstruction of objects (like destructuring first/rest from a sequence). Co-monads are basically objects!
