In case first-class continuations scare anyone away from Scheme: you probably will never use it directly in practice, unless you're doing something very unusual that happens to really need it.

For example, say you have a really hairy AI search algorithm, capturing a continuation happens to make backtracking easier.

Or you're implementing another language or DSL in Scheme, and you use first-class continuations to implement some control structure semantics exactly how you want them to be.

I think the closest I've used, in writing maybe a hundred modules, is an escape procedure (like a premature `return` statement in many other languages, which you generally avoid in idiomatic Scheme).