The question of “turn them off or let them burn” is a common one in lighting. Since there is no surge involved in the starting of any residential bulb, the answer is “if you are not using them, turn them off.” The cost of operating a light bulb is the wattage consumed while lighted thus the general answer is turn them off.
High intensity discharge lamps (rarely found in indoor household applications) and fluorescent lamps have different operating needs. If you have a fluorescent lamp, the general rule is turn the lamp off unless you are going to need it again within fifteen minutes. Frequent cycling, turning on and off for short periods of time such as in a closet application, can reduce the life of a fluorescent lamp.