Which of the following quantities remains the same as a metal ball is dropped and air resistance is neglected?

When a metal ball is dropped and air resistance is neglected, the only force acting on it is gravity. Gravity is a conservative force.

• A. Momentum: Momentum is $p = mv$. As the ball falls, its speed $v$ increases due to gravity, so its momentum changes. Therefore, momentum does not remain the same.
• B. Kinetic energy: Kinetic energy is $KE = \frac{1}{2}mv^2$. As the ball falls, its speed $v$ increases, so its kinetic energy increases. Therefore, kinetic energy does not remain the same.
• C. Total mechanical energy: Total mechanical energy is the sum of kinetic energy and potential energy ($E = KE + PE$). In the absence of non-conservative forces like air resistance, the total mechanical energy of a system remains constant. As the ball falls, its potential energy decreases, but its kinetic energy increases by an equal amount, keeping the total mechanical energy constant.
• D. Potential energy: Potential energy is $PE = mgh$. As the ball falls, its height $h$ decreases, so its potential energy decreases. Therefore, potential energy does not remain the same.

Based on the principle of conservation of mechanical energy, neglecting air resistance, the total mechanical energy remains constant.

The final answer is $\boxed{\text{C. Total mechanical energy}}$.