Lets say that your like Dropbox or Lastpass and you store users information in such a way that you can't open a users files.
There is only one real way to do this and that is for the user in question to hold and keep the encryption key and manage the encryption/decryption process. This means you need your encryption key on every device you wish to access the content, including any device on which you wish to use the convenience of the web interface, which is in my opinion why content-encrypted mail has failed to take off, since it makes web-mail difficult.
Otherwise, the option for the service provider is to encrypt your content - however, in order to give it back to you, the key must also be present in any delivery mechanism, meaning they might as well not bother.
A big clue as to who holds the encryption keys for your content is: can you access it via the web without supplying any key files? In the case of dropbox, you can make files available for public access, so, they either store these decrypted or else they have the mechanism to access them.
I said there is only one real way - a "fake" way would be to secure the generated key for that users' content with their password. This pushes the problem down the road, since for the duration of the session you either cache that password, its derivative, or the decrypted key for the files. Given this, I doubt it is used.
So I suspect your content (for a generic cloud provider) is either encrypted and stored next to the encryption key, or entirely unencrypted on their servers. Of the two, they do actually have a motivation to use encryption.
How would sites like Dropbox or Lastpass respond to a subpoena like this?
I assume they would hand over anything they had. I suspect this would be your encrypted content and their keys used to decrypt it, but assuming you had encrypted a file locally and not at any point transmitted the key to them, I would expect them to hand over the encrypted file along with everything else and provide evidence that they cannot in fact decrypt it.
What does their encrypting files protect me against?
The question you didn't ask - data stored on hard disks storing your files is, we assume, encrypted. Provided the keys are on a separate disk, throwing the file disk away (failure of a disk in their storage array, for example) ought to mean the content is reasonably protected. So encryption is worth their time, although it does not afford the protection most people imagine.