Is there is an API to retrieve the list of devices connected to the Ubuntu One service?
At Ubuntu One Account Page you can see the list and remove linked devices.
Obviously, API is here: UbuntuOne Admin API
Hovewer, there (Account info API ) such or at least identical feature is not listed.
Anyway for creating full access method to your account you should follow this note:
There is currently no public API for retrieving the list of devices programmatically. As noted above users can edit and unapprove devices from the U1 website or from the control panel.