Q:

Which directories contain system files?

When installing Ubuntu, I don't want to format the partition that is going to be /. Installation wizard prompts me that Directories containing system files (/etc, /lib, /usr, /var...) that already exist will be deleted. Can somebody list all of them? Does it include /home?

A:

Most directories contain 'system files', except those in /home/.  However, since you say your home directory is on the same partition, you would lose that data if you were to proceed.
When installing Ubuntu, you are given the option of having one partition for all directories, or mounting different partitions for specific directories.
One setup may have /, /bin, /home, etc on one partition, while another setup may have /, /bin, etc on a partition, with /home on another partition.  The benefit of the second setup is that you can re-install linux root (/) without touching your home directory (/home).
However, since you have the first setup, in this situation, you would be deleting all of the data on that partition, which includes your home directory.
If you have a LiveCD, you can mount your drive and move any data onto another HDD.  When installing Ubuntu, be sure to use the second setup to prevent this in the future.  Another option would be to place your HDD into another Linux machine, mount the HDD, and pull off the data.
Example:
I have an SSD (/dev/sda) and HDD (/dev/sdb).  When I install Ubuntu, I select to create an ext4 partition on all of the SDD.  I also create an ext4 partition on the HDD.  I then tell Ubuntu to use the SSD as the root (/) partition, and tell it to use the HDD as the home (/home) partition.
Tomorrow I accidentally run a bad command that I will not place here (let's say I just removed all the files in /bin/).  I can then load up an Ubuntu CD, format the SSD (/dev/sda1) partition, point to my HDD for home (without formatting).  After it installs, I will be on a fresh Ubuntu install with all of my home data.

