SSH automatic login without password

local> ssh-keygen -t rsa -f .ssh/id_rsa

-t is the encryption type
-f tells where to store the public/private key pairs. In this case, the .ssh directory on home is being used

A password will be asked; leave this part blank, just pressing <enter>
Now, go the .ssh directory, and you will find two new files: id_dsa and id_dsa.pub. The last one is the public part. Now, copy the public key to the server machine

local> cd .ssh
local> scp id_rsa.pub user@remote:~/.ssh/id_rsa.pub

Of course, this time you will need to enter the password.
Now, login into the server machine and go to the .ssh directory on the server side

local> ssh user@remote
remote> cd .ssh

Now, add the client's public key to the know public keys on the server

remote> cat id_rsa.pub >> authorized_keys
remote> chmod 640 authorized_keys
remote> rm id_rsa.pub
remote> exit

Actually in my case I had to chmod 644 for authorized_keys otherwise I was getting a password prompt still

SSHD is smarter than we think. The main criteria it seems to have is that authorized_keys must not be writable by anyone but the owner of the authorized_keys file, obviously to prevent other users from adding their own public keys and gaining access to another account :)