I have SSHed into a remote server from my phone out of necessity many, many times. When you get that e-mail on debian-security-announce that some package on one of your servers has just received a security update to fix some serious vulnerability, then ideally you install that update and reload the service right away, instead of putting it off for later.
When I had a Nokia N900, I programmed on the device all the time. Nothing especially big, of course, but the traditional-Linux environment and physical keyboard on that phone allowed you to quickly knock out a small shell or Python script if you had some task you wanted to automate.
