SSH as root to EC2 Linux instances

Assuming you are using the vanilla AWS Linux.

Start an editor, vi or whatever, and load the sshd config:
sudo vi /etc/ssh/sshd_config

Allow root login and password authentication by commenting/uncommenting:

…
PermitRootLogin yes
# Only allow root to run commands over ssh, no shell
#PermitRootLogin forced-commands-only
…
# To disable tunneled clear text passwords, change to no here!
PasswordAuthentication yes
#PermitEmptyPasswords no
# EC2 uses keys for remote access
#PasswordAuthentication no
…

Reload the sshd settings:
sudo service sshd reload

Select a password for root:
sudo passwd root