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Ansible is trying to connect as root, as it seems you are running it as root. Are you sure the key you created was for the root user, and its the same you included through the control panel?
A better long-term approach is to create a user in the server the reflects the user you have in your controller machine - Ansible tries to connect using the user you are usually logged in. This should not be root… You give this user permission for sudo, and then you will be able to run commands and playbooks as normal user, asking for sudo when necessary.
Be sure to pass the -u flag with a user. This should be the same user you added the key to on the droplet.
ansible all -u $DROPLET_USER -m ping -i hosts
<blockquote>debug1: Next authentication method: publickey <br>debug1: Trying private key: /root/.ssh/id_rsa <br>debug3: no such identity: /root/.ssh/id_rsa <br>debug1: Trying private key: /root/.ssh/id_dsa <br>debug3: no such identity: /root/.ssh/id_dsa <br>debug1: Trying private key: /root/.ssh/id_ecdsa <br>debug3: no such identity: /root/.ssh/id_ecdsa </blockquote> <br>Do you have an ssh key generated and stored in ~/.ssh?