There was a whole raft of discussions in 2006 on Lambda the Ultimate and elsewhere about using continuations for page flow in webapps, and ultimately the most persuasive argument (against) was that continuations implied linear flow whereas web-page flow could be non-linear, what with the back button, hyperlinks, and all that.

However, I think that continuations are still very cool, and are especially cool when they can be serialized or written to disk/transmitted/etc., because this essentially lets you "time/space-shift" your thread/process, since it's just bits.

Right now, "suspending" a process is something that happens when you close your laptop or pause a VM, but I think that being able to do this at a much more fine-grained level of detail is what will allow general cloud-based computation to really take off, because individual threads would be portable across computing environments.