VMware offers a wide range of management tools, with over lapping capabilities. ESXi v5 includes a pretty useful shell on the actual VM host. VMware also provides an appliance "vMA" that is setup with all the remote CLI tools.
The vMA appliance at MSU is msu-vma.msulocal. There is a non-privileged account for normal use. Can put ssh keys in it for easy access.
ESXi VM hosts
The ESXi hosts have ssh enabled, but only allow ssh_key access (just as done on most normal cluster servers). The keys for the root account are stored in /etc/ssh/keys-root/authorized_keys