Bitcasa

Bitcasa is an app that allows you to back up your files, sync your data, and access your files from any of your computers.  Stored on a cloud server, Bitcasa will enable you to access your files from your computer, your tablet, or your mobile phone.

Features:

• Storage is Infinite.  Bitcasa stores your files on a cloud, which saves you space on your personal equipment.  Not having to store all your files saves your storage space for other things that may be essential for you to have, that may not be backed up on a cloud server.
• Internet connection is not required.  If you don't want to depend on an internet connection, or you know you'll be somewhere that doesn't have internet access, you can sync your files prior to this, and have your files on your specific platform for you to access when you need them.  The changes that you make can then be backed up to the Bitcasa server once you obtain an internet connection again.
• Access your files on PC, Tablet, or Mobile Phone.  The Bitcasa system is designed for Windows and Android systems.  This allows you to access your data, whether you're at home in front of your computer or stuck at an event away from home with your tablet or mobile phone.  You can work with your files from nearly any location, or on a variety of devices.  
• AES-256 Bit Encryption.  To put it basically, your files are protected from people who you don't want to have access to your files.  If someone attempts to breach your data without your permission, the Bitcasa encryption will protect you from sharing your work with others.

Bitcasa allows you to access, back-up, and sync your files, wherever you may be.  It is a relatively fast service, for what you're asking it to do.  If you're looking for a cloud service for your PC/tablet/mobile device, take a look at Bitcasa, as it provides everything you are looking for in a service.

You don't need to have an internet connection to access your information.