Continuations that are not single use are usually called multi-shot continuations.
Single shot continuations are very useful though. They are enough for a very large percentage of the situations you would use continuations for while being much more efficient to implement (no need to save the stack)while also being more reasonable theretically in other situations(call/cc can be used to break some important invariants when it interacts with mutablestate and other things like that. Its kind of subtle)
http://c2.com/cgi/wiki?SingleUseContinuation