Is there anything like Carbon Copy Cloner (CCC) for Linux?

CCC is just a fancy front-end gui for rsync. I'm not sure if there is an equivalent for linux, but if you don't mind the command line, you can do what you want there:

rsync -a -x / /media/backupdisk/

Replace /media/backupdisk/ with whatever mount point your backup disk is attached to.

If you want the backup disk to be an exact copy, add the --delete flag:

rsync -a -x --delete / /media/backupdisk/

It's true that CCC is just rsync on the inside, but there is a lot more going on inside. I tried using rsync and it's not easy to make a fully functional and bootable copy every time.

If you want to make an image (byte for byte) you can always use dd.

dd (Unix) - Wikipedia