I first stumbled on this pattern when designing a replacement for a feed processor at the BBC. The basic task was to process a feed of information snippets encoded as XML and generate/update web and interactive TV (Ceefax) pages.
Like a good little enterprise architect, and similar to the existing system, I had originally planned to use a central SQL database for storage, though designing a data model for that was proving difficult due to the highly irregular nature of the feed data. As an auditing/logging measure, I also wanted to keep a copy of the incoming feed data, so when the time came to do the first implementation spikes, I decided we would implemented the display, update and XML feed processing logic, but not the datastore. Instead, we would just re-play the feed data from the log we had kept.
This worked so well that we never got around to implementing the central database.
Leaving out the database vastly simplified both our code-base and the deployed system, which I could run in its entirety on my 12" AlBook whereas the system we were replacing ran around a dozen networked machines. Apart from making us popular with our sysadmin team both in terms of reliability and deployment/maintenance complexity (essentially a jar and a working directory was all it needed), a fringe benefit was being able to work on the system on said AlBook while disconnected from the network, working from home or from a sunny patch of grass outside the office.
In addition to personal happiness, systen performance was also positively affected: since we kept our working state completely in memory, the AlBook mentioned outperformed the original cluster by 2-3 orders of magnitude, producing hundreds of pages per second versus taking from several seconds to several minutes to produce a single page.
Performance and simplicity are exactly the benefits claimed for prevlayer, a persistence layer for Java based on the same principles.
TeaTime, the theoretical foundation and actual engine working underneath Croquet, takes this idea to a whole different level: objects do not have state, but are simply names for message histories. This is truly "objects [and messages] all the way down". Turtles need not apply.