I don't think you have it quite right.
The whole idea of 'off site', or 'cloud storage' is to have a file(s) stored on this 'community' hard drive, so you can get it back at any time.
In theory, you (or anyone) with the correct credentials, can access the files and retrieve them. Having them on your own drive is not a requirement.
There are however varying degrees of security of those 'community' hard drive services, and Drop Box has been less than ideal.
Anytime you entrust someone with your files, you must have absolute certainty that the files can never fall into the wrong hands (by the service 'snooping' or if they get 'hacked').
Here's one:
25Gb @ Skydrive.
From Microsoft.
http://skydrive.live.com/
Free.
If you have Zone Alarm firewall, there's now a free, 2Gb cloud storage.
Premium services also available.
For max security, data should be encrypted before sending, independent of any site involvement with that phase.
Use a solid 'on-board' utility for this, and practice a couple of times with some nondescript file to master the entire process so you know for certain you can get your files back.
That would be: file encrypt> upload>download> decrypt & verify.
Once proficient, go ahead with the more delicate file work.
[AxCrypt is an easy to use file encryption program. It integrates directly with Windows Explorer, enabling encryption, decryption, viewing and editing of any file with just a few clicks of the mouse. AxCrypt uses 128-bit AES encryption and SHA-1..."etc. Freeware. http://www.snapfiles.com/Freeware/security/fwencrypt.html ]