How to SSH Login without password on Ubuntu Server 13.10

SSH offers a secure connection to a remote server. But sometimes we need to login to remote server via SSH that does not ask for password. This task will be useful when we want to backup remote server via SSH using rsnapshot. So, on this tutorial, I am going to show you how to login to remote server via SSH without password. 
On this tutorial I am using two computer. The first one, local computer, called dhani-ubuntu (192.168.2.103) and the remote server called ubuntu-server (192.168.2.109). 
First, open Terminal and we need to generate public and private key using ssh-keygen. 

dhani@dhani-ubuntu:~$ ssh-keygen
Generating public/private rsa key pair.
Enter file in which to save the key (/home/dhani/.ssh/id_rsa):
/home/dhani/.ssh/id_rsa already exists.
Overwrite (y/n)? y
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /home/dhani/.ssh/id_rsa.
Your public key has been saved in /home/dhani/.ssh/id_rsa.pub.
The key fingerprint is:
61:6f:6e:5b:9c:c9:66:56:01:0d:44:0f:13:d1:67:e8 dhani@dhani-ubuntu
The key's randomart image is:
+--[ RSA 2048]----+
|           oX* . |
|             =+ o|
|        o    .oo |
|       . o    E. |
|        S o   .  |
|         o o +   |
|          o X    |
|         . *     |
|          .      |
+-----------------+
When you enter ssh-keygen command you will be asked to enter the passphrase. Since we want to login without password, do not enter any passphrase here. Simply press the Enter button twice and you will be done. 

Next, we need to copy this new public key to the remote server. 
dhani@dhani-ubuntu:~$ ssh-copy-id -i ~/.ssh/id_rsa.pub 192.168.2.109
/usr/bin/ssh-copy-id: INFO: attempting to log in with the new key(s), to filter out any that are already installed
/usr/bin/ssh-copy-id: INFO: 1 key(s) remain to be installed -- if you are prompted now it is to install the new keys
dhani@192.168.2.109's password:
Number of key(s) added: 1
Now try logging into the machine, with:   "ssh '192.168.2.109'"
and check to make sure that only the key(s) you wanted were added.
Ok now we can check to login to the remote server using ssh. You should not be asked for a password.