Fan limit is important, it is not recommended to operate the fan without the fan limit. Without the fan limit control your fan could over heat and cause a fire!
The fan limit switch is a safety control which protects the heat exchanger from damage (such as heat exchanger cracking due to overheating).
The limit control is an electrical switch that opens when the temperature around it gets above the setpoint. Some are a round button-like switch and are referred to as snap disc limit controls. Others have a long metal sensor or a long mounting arm with a snap disc on it. On older furnaces, the control also turns the blower motor on and off at a preset temperature. These are referred to as fan/limit controls.
See Limit Control Replacement Procedure at hvac-for-beginners.com.