If you have a large number of ESXi hosts that you need to SSH to and they have various passwords and so on, (this is not super secure, so do at your own security assessment)
Just like you can do this on a Unix host, you can do the same for ESXi:
1. Generate a Public/Private key on the linux host:
ssh-keygen -t rsa
This will create two files in ~/.ssh: id_rsa and id_rsa.pub.
In ESX 5.X, the location of authorized_keys is: /etc/ssh/keys-<username>/authorized_keys
So you can do this:
scp /root/.ssh/id_rsa.pub remote-ESXi-host:/etc/ssh/keys-root/authorized_keys
Like this for example:
scp /root/.ssh/id_rsa.pub 192.168.3.102:/etc/ssh/keys-root/authorized_keys
Of course if you want to do this from more than one host, then just add to the authorized_keys file rather than overwriting it....