VMware ESXi is UNIX like but at the end of the day is an appliance with many limitations. Since its based on Linux we still have a number of tricks up our sleeve.
SSH by default is disabled on VMware ESXi. Turning it on is just as easy as un commenting the ssh line in /etc/inetd.conf and restarting /sbin/services.sh. VMware uses the dropbear ssh client and there is no configuration file on the system.
To create an ssh trust on ESXi do the following. Create a .ssh directory off of the root directory for the root user. Create an authorized_keys file in this directory. Copy your public key to this file on the system and you have your root trust. The next time you log in you won't be prompted for a password and you can run remote commands on your ESXi system.