We had a sysadmin that spent most of his time on 2 tasks, 1 was an internal maintenance task, and the other was email.
When he quit, those tasks fell to me, the sole programmer at the time. THe internal maintenance task, I did it for about a week before I decided that it needed to go away. So I wrote scripts and an interface for it, tested it for a while, and turned it over to customer service, which was the department that was requesting it anyhow. They were ecstatic because it meant they no longer had to request it and wait... They could just do it instantly. Much better for everyone.
The email was easier. We just moved to Google Apps.
The remaining tasks that the sysadmin did were now just a tiny fraction of my time.
As the company grew, those tasks increased until management realized they needed an actual sysadmin again, and they hired one.