I remember that Ubuntu One could do that back in the days when it has storage features. Dropbox just syncs are folder with it Linux client. When using Google Drive with Grive2 it should be possible sync only the EncFS encrypte folder. Are there service that support that out of the box?
All the cloud storage services like DropBox basically mirror a specific local directory, so anything you can do with a local directory & files (sparse files and some file attributes might be problems) you can do with your local copy of cloud files. There were a couple that are supposed to support built-in encryption, but they hold the files and it's their software, so ultimately they control the security
Using just about any encryption should work, a LUKS/dm-crypt container, an EncFS folder (it may not be the best for cloud storage, see below), or an eCryptfs folder (though it usually keeps config files separately in
/home
), or CryFS is new & appears specifically designed for cloud storage.