Memopal recently released a version of its software for Linux, offering an online backup service for either personal or business users. The business service allows multiuser access, so it can act as a filesharing as well as a backup service. You can get a free trial access for 7 days, but after that it's (unsurprisingly!) a paid-for service.
The Linux version is still in beta and has only a command-line interface. It's available for Ubuntu, Debian etch, and Fedora binaries only, not source code, as it's not open source. The online documentation is limited, but support is available via the Web site, and there's a community forum that seems active.
My 5MB test backup took about five min. After it completes the immediate backup, the program keeps running, and as I understand it, it should watch for changes and then back those up. However, in practice it didn't spot my test file creation until I restarted the backup.
I couldn't see an automate option possibly this is part of the GUI and thus not available for Linux. You could set up a cronjob, but be wary that it requires your password as plaintext to run. The command is
memopal -u username -p password --backupFolder /full/path/to/directory
Default output is pretty verbose, outputting a line every second.
For file restore or file access, you can browse your files directly from the Memopal Web site a really nice feature, which also enables you to check your backups straight away.
It's definitely got promise, and may be worth experimenting with for essential files but as an always-on daemon type of backup I don't think it's quite there yet for Linux.