I have two questions...
Firstly, is the communication between my Ubuntu desktop and the Ubuntu One cloud encrypted?
Secondly, are the files, media etc. stored on my Ubuntu one account encrypted on the servers?
Regarding the communication with the cloud, yes, SSL is used, it's described at https://one.ubuntu.com/privacy/ .
About storage encryption, it is not specified on the privacy statement, I remember reading somewhere that it is not encrypted. Anyway you should be able use encfs or other file based encryption mechanism.
Update: I have found the following answer about successfully using encfs with Ubuntu One: https://answers.launchpad.net/ubuntuone-client/+question/74734
Update2: A full guide explaining how to do per file encryption in UbuntuOne can be found here
Update3: The official word is that storage is not encrypted.
This bug contains a good explanation of the state of encryption in Ubuntu One at the moment: https://bugs.launchpad.net/ubuntuone-client/+bug/375289