I created the RSA key and uploaded it to the remote machines I wanted to SSH to. However, I realized that, on my local machine, I can SSH straight in without entering my passphrase. On the remote machines, when I want to SSH to another, I have to enter my passphrase as expected.
I don't seem to be running ssh-agent or ssh-ident (or at least running 'service ssh-agent' returns unrecognized service). What could be allowing this to happen? I'd imagine that the passphrase must be stored somewhere, and if it's in plaintext I'd like to disable this function.