So I've been playing with QEMU, which lets you run a virtual computer inside your normal computer. At the moment I'm using it to create a reproducible development environment on a project I'm working on.
Among QEMU's features is the ability to save a virtual machine snapshot, which includes the entire state of the virtual computer: memory, CPU, even disk. This seems similar to KeyKOS's checkpointing facility, although it seems to be a bit slower, maybe to the point of being less useful. (It seems to do all of its I/O before continuing to run, rather than doing some kind of copy-on-write. It seems like fork() might be sufficient to get good copy-on-write performance.)
(In one case, a VM snapshot of a 128MB VM took 53MB of space.)
But suppose you ran your normal GUI session inside of QEMU. Maybe every few minutes, you could do a backup of your live session to a server somewhere nearby.
If you do this, you can transport your GUI session from one machine to another --- something the term "VNC", an abbreviation for "Virtual Network Computer", promised but never delivered. If your machine ever crashes or gets stolen, you can restore from the previous checkpoint; sometimes this might be worth doing even if only a single application within it has crashed. And you can have a large number of GUI sessions for different users in suspended animation on your disk.
This kind of thing could give users in, for example, an internet cafe, the freedom to really customize their environment. Rather than storing all of their state on a web site, they could store much of it on the servers at the internet cafe itself, as if they owned it. They could install software, keep their files, and so on; and whenever they came into the cafe, their session would be waiting for them, just as it was when they left it.
There are a lot of times these days where you'll want to run stuff that doesn't run very well inside QEMU: MPlayer, Art of Illusion, anything with SSE, MMX, or 3-D acceleration. I think that's kind of a minor problem, since the data involved in that part of the system (the latest frame of a movie, say) is usually quite transient and easy to recreate.
Also, it's not uncommon these days for a GUI session to fill up gigabytes of RAM, and all of that RAM could in theory change its contents about once a second. So you still might end up copying all or the vast majority of the memory pages during a snapshot.