On most modern computers, there's an energy saver preference which will shut down your hard disks when the computer is idle or in "sleep mode." On a Mac, this is enabled by default in System Preferences --> Energy Saver.
I had been puzzled as to why CrashPlan, in my case, wasn't backing up remotely overnight... it did a grand total of about 20 files... If you want to enable your backups to run while you sleep, make sure your hard drives don't sleep.
Untick the checkbox in the Energy Saver window that says "Put hard disks to sleep when possible," and your backups should now continue to run as long as your Mac is alive and waking.