I came across an interesting article on oDesk that discussed cloud services for user data and had some links to various services that do what I want.
Below is a list of cloud services for storage and synchronization of user data, taken from the oDesk article:
- Apple's iCloud (iOS and Mac Only)
- Dropbox Sync
- Simperium
- Parse Data
Note that iCloud and Dropbox require accounts through their own systems, while Simperium and Parse let you set up and manage your own user accounts through their services.
Simperium at least seems a great fit for storing user data in the cloud.
Another interesting article I found was case study about Simperium describing how their cloud app Simplenote originally used Google App Engine to provide their cloud synchronization and storage.
So it seems that Google App Engine/Cloud Storage can also be used to provide good synchronization and storage for an app.