One really nifty use case of continuations is the Seaside Smalltalk web framework [1]. It implements stateful request/response conversations with Smalltalk's ability to capture and serialize continuations.
Continuation-based web frameworks are really nifty, but have potential scaling bottlenecks. IIRC HN originally used some type of continuation web framework with Arc, but ran into scaling and caching headaches. Dunno how it works these days.