Backup MacBook Pro to USB-Stick in Single User mode

mbpusbbackup.txt

Create a hfs+ usb stick on Ubuntu:
sudo apt-get install hfsprogs
sudo apt-get install gparted
using gparted, create a partition table and a partition, format the partition table to hfs+

Boot the MBP to Single User Mode using ⌘+S key on power on
When booted:

/sbin/fsck -fy
/sbin/mount -uw /

ls /dev/disk*

plug the USB stick into your MBP
ls /dev/disk* 

compare the output with previous ls /dev/disk* output, there must be a new disk like disk2s1/disk2s2

fsck_hfs /dev/disk2s2 (your disk name goes here)
mkdir /Volumes/usbdrive
mount -t hfs /dev/disk2s2 /Volumes/usbdrive (again, your disk name goes here)

rsync -av /path/to/sourcefiles/* /Volumes/usbdrive

umount -f /Volumes/usbdrive