In my early days of CIVing (I and III), I'd automate everything, thinking that the AI would be more efficient than doing it myself. Which was true, problem was that I didn't understand the subtleties to managing workers and manipulating production. After reading Cracker's Civ3 Opening Plays Site in the War Academy, I'll never automate again. The closest I get to it is managing moods via the governor but I will move workers manually and switch often between emphasizing production, food and commerce via the governors.
If more people read this, Firaxis would have to come up with a tougher challenge, because scores would soar. This is inside-type information including information on how the AI really works and how it compares to other strategies of city production. Very complex and very insightful.
But getting back to the question...I'll never automate workers again.

Like he said on his very lengthy "Opening Plays Site", you sign your death warrant when you automate!
In short, the AI works with a narrow "window" of view...it only considers those tiles within the initial eight-square ring and doesn't anticipate beyond that. If you read this piece, you'll never automate again, except for maybe happiness via the governor (that's a pain!).
For those of you disappointed in the "Strategy Guide" for CivIII that's currently on the market...these articles in the War Academy, particularly this one and others written by Cracker are must reads for anybody serious about learning the game not only from the human perspective, but also from the AI perspective! Unbelievable stuff!