Coroutines are quite nice for managing sessions with asynchronous events, like stateful GUIs or client-server interactions. If you're familiar with the tendency of callbacks in e.g. JavaScript to nest deeply, you can think of coroutines as a way to recover a flat, procedural style.

I'm a particular fan of how coroutines work in Lua. Here's an article that helps explain them a bit in that context: http://leafo.net/posts/itchio-and-coroutines.html