To truly secure your data in the cloud it is necessary to encrypt it before it leaves your computer and not to trust others to do this for you. You can encrypt files yourself with something like Truecrypt, DiskCryptor or 7Zip but it requires time and extra work.
This list contains cloud storage services that apply encryption before uploading it to their servers and give you full control of the decryption keys, making it impossible for the company to decrypt anything.
TeamDrive: Company based in Germany, data is encrypted in the computer with AES256-bit using your own encryption key that the company has no access to. You can decide whether to store your files in Amazon EC2 USA, Ireland or Hong Kong servers, account data is only held in German servers.
Mega: Based in New Zealand, all data is encrypted with AES128-bit before uploading it to the cloud, a RSA2048-bit key is used to share already encrypted files in between users, their FAQ is very complete explaining the security measures they use and what possible vulnerabilities exist against their business model.
Powerfolder: German company, it can be used to store and share files in the cloud, they have no servers in the USA and everything is encrypted client side with the AES algorithm. You can password protect folders before sharing them with others.
TresorIt: Hungarian company, they use AES256-bit to encrypt data before uploading it to the cloud. The company offered $US10.000 to whoever can break their security software. Data can accessed in your smarphone or desktop computer. There are free and paid for plans.
Notice: Even if the company is not based in the USA, they might be using American servers for storage unless specified.