People keep mentioning this. What are some real-world uses for this feature? Who is using CouchDB in this fashion, and what are they doing with it?

Here's a CouchApp that (with a non-demo dataset) we use internally for TODO management. I have a copy running on my laptop, on my MacMini at home, on the office server, in the cloud, and of course, on my Android phone. I synchronize them when I feel like it (but I could configure it to continuously synchronize in the background).

http://couchapp.couchone.com/focus/_design/focus/index.html#...

For more info on the method of serving HTML5 apps directly from CouchDB's web-server: http://couchapp.org/page/what-is-couchapp

One example of CouchDB offline replication:

http://one.ubuntu.com/

Of course, data synchronization is never automagic—the dirty little secret of all distributed systems. Merging is hard!

In CouchDB's document model this manifests itself as the challenge of of deciding how to split the results of user interactions across documents. Eg: don't store comments on the blog post document, keep them on their own documents, as they have different update patters. Of course this pattern doesn't answer everything, but it gets the vast middle of use cases.