Which gauge on the instrument panel indicates how many miles a vehicle has been driven?

The odometer is the gauge that records the total distance a vehicle has traveled in miles since it was manufactured. This information is essential for tracking the vehicle's usage and determining maintenance needs. Unlike the speedometer, which indicates the current speed of the vehicle, the odometer provides a cumulative measurement of distance.

The fuel gauge shows how much fuel is left in the tank, while the temperature gauge displays the engine's coolant temperature, indicating whether it is operating within a safe range. These functions are important but do not relate to distance traveled. Thus, the odometer is the specific instrument designed for measuring and displaying the total mileage, making it the correct answer.