For example, you could store your data locally in an appliance like the ioSafe N2. The NAS (network attached storage) device can hold terabytes of data in a redundant configuration inside a fire proof, flood proof enclosure. Best of all, the N2 connects to the network and to the Internet, and it makes the data available from virtually anywhere, and from any computer or mobile device.
Another option is to choose a hybrid cloud solution like Egnyte. Egnyte does provide cloud file storage, but it can also connect and sync with local storage platforms.
Just keep in mind that this approach has tradeoffs. In order to gain greater security and privacy, you have to take responsibility for managing and maintaining the servers and data, which is arguably one of the biggest benefits of cloud services for small businesses. Also consider the fact that the third-party cloud support personnel might know more than you do about security and privacy, so managing it yourself may give you an illusion of greater security and privacy, while actually putting your servers and data at greater risk.
Sign up for CIO Asia eNewsletters.