Earlier quoted context omitted.
Errors/exceptions, for one, are implemented using continuations.
Sounds terribly inefficient to me, but what do I know -shrug-
In a web app context, though, it's kind of silly to keep a stack around to handler something like clicking a link that returns the contents of database row foo. People do this, call it continuations, and then run into problems. The problem is not continuations, the problem is that you are treating HTTP as a session, not as a series of request/responses. (The opposite of this style is REST.)