Every backup service worth its salt uses encryption to keep your data safe from snoops, but SpiderOak goes one step further by promising to keep your data private from its own employees. Although you still should use common sense in choosing what to upload to any service, I believe that SpiderOak is one of the best secure online backup options available.
You may store up to 2GB on a free account; extra space costs $10 per month or $100 per year per 100GB (cheaper than Dropbox but a bit pricier than Mozy).
You download an application (for Windows, Mac, or Linux) that coordinates which files and folders to back up, and runs in the background to sync your online backup with your PC. The password that you create never goes to the SpiderOak servers; it's stored on your PC. Your password then serves to generate a pair of encryption keys, which also remain local. The keys work to encrypt your files on your PC before the data goes to the SpiderOak servers--without your password or keys, no one can view your data without cracking the encryption via brute force.
This hands-off approach means that every time you log in to SpiderOak, you're just verifying your identity to the desktop client, which in turn establishes a secure connection to the SpiderOak servers. As long as you never log in via SpiderOak's website or a mobile device (in addition to the desktop tools, SpiderOak offers mobile and Web clients for convenience), your password will never enter SpiderOak servers, so theoretically it's difficult for a SpiderOak staffer to peek at your data or give it to a third party.
Of course, since SpiderOak doesn't store passwords, it can't help you recover a forgotten one. You can store a password hint on the SpiderOak servers, though. Remember, if you lose your password, your backup becomes unintelligible (unless you want to try breaking the 256-bit AES encryption yourself).