"The only time that you would not want to move a wounded unit to a barracks in Civ3 is if it only has 1hp in damage."
Just a minor correction... When a wounded unit has TWO hp of damage, I will often not move it to a barracks either. If you move on a turn, you can't heal that turn. So moving to the barracks would take 1 turn, and another turn to heal the two points.
However, if you just fortify the unit, it will heal 1 point the first turn and another point the second turn. So you would heal just as fast by simply fortifying the unit.