Backing up microSD Cards is good practice. This is how I do it. But backup is the wrong term. I am actually creating an image that can be loaded on a new microSD Card.
To create a backup, use rsync. I think it would be great backup a Raspberry Pi to a USB Drive without shutting down the Raspberry Pi or removing the microSD Card, and have this done periodically via crontab.
PyMyLifeUp: See instructions with this header: Backing up your Raspberry Pi to a USB Drive
Parts:
Raspberry Pi
USB microSD Card Reader
Step 1. Get the microSD Card
Shutdown the Raspberry Pi
$ sudo shutdown -h 0
Remove the microSD Card
Put the microSD Card into a USB reader
Step 2. Make a copy
Put the USB device in a MacBook and make a copy of the image
On a MacBook, open a terminal window and run the command
$ diskutil list
/dev/disk5 (disk external):
Identify the USB device. It should be marked as external.
I keep backups in my Downloads directory on my MacBook
Run a command similar to the following. rdisk is important on a MacBook:
$ sudo dd if=/dev/rdisk♣your-usb-disk-#♣ of=/Users/♣your-account♣/Downloads/♣image-filename♣
Step 3. Put the microSD Card back