Some more esoteric suggestions:
Idle workers could act as...
Spies, by running around with Open Borders.
Scouts, by moving through the fog of war. Don't do this if there are Wolves or Panthers running around.
Lookouts, by sleeping on a hill where it has great visibility (you need this to be safe).
Good Will Ambassadors, by helping your allies with repairs.
Lumberjacks, by chopping down far-away forests and jungles.
Prospecting, by building mines everywhere.. (you have a small chance of discovering rare elements.)
Or, you could build a road in every tile!
Just be careful with your unit costs and unit supply.