The name of the program causing Nautilus to show partition in the left side bar is gvfs-gdu-volume. To kill this process, run this command to see the PID of the program
sudo ps -e | grep gvfs-gdu-volume
In my system, the output is
6642 ? 00:00:00 gvfs-gdu-volume
So, I know the PID is 6642, it may vary by time to time.
Kill that process with
sudo kill -9 PID-of-gvfs-gdu-volume.
Or as a one liner, try this
sudo kill -9 `ps -e | grep gvfs-gdu-volume | cut -f 2 -d ' '`
Open nautilus to see the magic !

This image is from thunar in Xubuntu 12.04 LTS.

Note: The solution isn't permanent. Whenever you open a file in Gedit or something like that, The drive icon all appears again. To permanently disable this, follow the below work around.
Workaround to disable this permanently.
Open a terminal and do this command:
sudo mv /usr/lib/gvfs/gvfs-gdu-volume-monitor /usr/lib/gvfs/gvfs-gdu-volume-monitor.bak
This command renamed the culprit file to show the drive icon with adding a .bak extension. That's it.
If you want to revert the change, use this command
sudo mv /usr/lib/gvfs/gvfs-gdu-volume-monitor.bak /usr/lib/gvfs/gvfs-gdu-volume-monitor
Note: This is not a decent solution, but this works perfectly, and I am happy with this.
My drive icon has gone, How can I mount them now
Don't cry. Here is your trusted friend terminal. Open a terminal and do this command to mount /dev/sda1 partition. It will do what nautilus does.
udisks --mount /dev/sda1
To find the /dev/sdaX number of desired partition, do sudo blkid on the terminal.
Update for 12.10
It seems Ubuntu 12.10 is using udisks2 program and the responsible program for showing the drive icon is also changed. It is now gvfs-udisks2-volume. You should kill this process instead of older gvfs-gdu-volume program.
2: 1: https://i.sstatic.net/WIjuK.png