Q: We use nuclear forces to create energy. Likewise can we harness gravity too?

Krishna: Absolutely! We can use the force of gravity for the benefit of mankind. Here are a few examples:

Gravity has actually been, from all the fundamental interactions, used as means of producing and storing energy. Water turbines, windmills, clocks powered by weights on ropes are all devices that use gravity, directly or indirectly (as in case of wind, which actually comes about by combination of gravity and solar energy). We call it by different names such as hydroelectric and wind. But without gravity, there wouldn't be pressure at the bottom of a dam to turn a turbine. The atmosphere would drift away - nothing to turn windmills.Gravity even makes the winds blow.

Gravity energy creation in hydroelectric powerstations—they usually have an upper reservoir, and a lower reservoir.

If you open the gates between these two reservoirs, water flows downhill (converting gravitational energy into kinetic energy). You can then place turbines into the path of the water, and use the rotation of the turbines to produce electricity.

Gravitational energy in the water, converted into electric energy.

The gravity light is an interesting project. 

Elevator technology utilizes gravity to generate power (RegenDrive - Otis Elevator Company - China ), which helps reduce overall energy consumption and costs.

HOW AN ELEVATOR CAN PRODUCE POWER?

A conventional elevator system consists of a car, a machine and a counterweight. The counterweight is designed to balance the weight of a half-loaded car. As a result, the counterweight is heavier than an empty or lightly loaded car, but lighter than a heavily or fully loaded one. This difference enables the elevator to utilize gravity to travel up with a light load or descend with a heavy load. When the car utilizes gravity, the machine creates electricity just like a generator. In conventional systems, the electricity generated by the machine is wasted. It is fed back through the elevator electrical system and dissipated as heat through resistors, creating waste-heat loads in the building. ReGen drives conserve this energy and put it to work.

Combined with highly efficient gearless machines, ReGen drives feed this energy back into the building’s electrical grid where it can be used to power other building systems.

Diagram depicting how the Regenerative Drive sytem works. Image credit: Otis Worldwide

You can indeed harness the energy of gravitation and it is done on a somewhat small scale, as the main method to do it is to use the tidal movements of water. Most places do not get particularly impressive tides, so it remains a rather minor method of producing energy.

And this one is very interesting...

We also harness gravity in space travel. From the Hohmann transfer orbit 

(In orbital mechanics, the Hohmann transfer orbit  is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane.

The orbital meneuver  to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it. )

to Gravity assist ( In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically in order to save propellant, time and  expense. Gravity assistance can be used to accelerate a spacecraft, that is, to increase or decrease its speed and/or redirect its path. The "assist" is provided by the motion of the gravitating body as it pulls on the spacecraft. )

to Lagrangian points ( 

In celestial mechanics, the Lagrangian points -  also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies. The Lagrange points mark positions where the combined gravitational pull f the two large masses provides precisely the centrifugal force required to orbit  with them. There are five such points, labeled L₁ to L₅, all in the orbital plane of the two large bodies. The first three are on the line connecting the two large bodies; the last two, L₄ and L₅, each form an equilateral triangle  with the two large bodies. The two latter points are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.

Several planets have satellites near their L4and L5 points (trojans)  with respect to the Sun, with Jupiter in particular having more than a million of these. Artificial satellites have been placed at L₁ and L₂ with respect to the Sun and Earth, and Earth and the Moon, for various purposes, and the Lagrangian points have been proposed for a variety of future uses in space exploration.

to the Interplanetary Transport Network, interplanetary space travel is largely a matter of sophisticated exploitation of gravitational fields, and this has been true since the early days of space travel. This was why William Anders , Lunar Module Pilot on the Apollo  mission, said on mankind’s first journey to the Moon : “I think Newton is doing most of the driving right now”. And he was right — the Apollo missions all used Hohmann Transfer orbits for the Earth-Moon transit.

According to some physicists ...

Gravitational potential energy is the energy associated with the system of a heavy object. It is not actually located right within the object - rather it is situated in fields. But still for the near earth objects we can deal with the things even if we consider a model in which the particular objects possess some gravitational potential energy in them. But the real problem is - once you use the gravitational potential energy of an object to do some task, there is no more gravitational potential energy in the object that you can use. You need to lift the body again to some level and then you can use the increased potential energy, but obviously you provided the object some energy when you lifted it. That is why it is a bit difficult to harness this energy.

Gravity seems an infinite source of energy on naive analysis because we think gravity is always there, why isn't it an everlasting source of energy? The reason is,  gravity is essentially a force continuously acting downwards it will take energy from you while you are moving the object upwards and will return you the same energy when the object is moving down. If any object is already at some height, once you get some energy from it but then again you have to perform work to take it to some heights.

Gravity could have been a great source of energy if it would be like a huge bunch of matter is naturally situated at great heights and you make it fall and use the energy and yet there is much matter at heights which you can further use. And in a sense, that happens in the hydraulic power plants.