Adding public key to ~/.ssh/authorized_keys does not log me in automatically

You need to verify the permissions of the authorized_keys file and the folder / parent folders in which it is located.

chmod 700 ~/.ssh
chmod 600 ~/.ssh/authorized_keys

For more information see http://www.openssh.org/faq.html#3.14

You may also need to change/verify the permissions of your home directory to remove write access by others.

chmod go-wrx ~