A negative feedback loop is when the output of a system acts to oppose the input of a system, forcing the system back to it's original state. This is extremely important for the preservation of natural systems on Earth, such as the Nitrogen Cycle or the Water Cycle.
Another, albeit much stranger, feedback loop doesn't occur on Earth at all. It occurs only in the deepest vacuum, when there are no other particles.
Virtual Particles are the manifestations of "vacuum energy" that is found in the space where the vacuum is. Because energy can turn into matter, via Einstein's Theory of Relativity, the vacuum energy turns into two opposing Virtual Particles: A piece of Matter and Anti-Matter. The two particles have a mass, exist in time, and once are created destroy each other and return to being energy.
This can be tested in a lab using a vacuum and two metal plates parallel to each other. When the vacuum is created, the vacuum energy begins to form into virtual particles. The visual effect is that the two metal plates will slightly bend away from each other as the force of the Virtual Particles coming into and leaving existence push the bars apart.
Virtual Particles are a great example of a negative feedback loop because it demonstrates a return to the original form that the system starts in. First we have a vacuum, followed by the creation of particles, the destruction of particles, and then a return to a pure vacuum state again.
These virtual particles are the same as described in Stephen Hawking's Black Hole Theory and the presence of "Hawking Radiation". Hawking described Black Holes as having a spout of particles coming out of it from both sides even though a Black Hole is supposed to absorb everything. What Hawking deducted was that these virtual particles were forming at the event horizon, or 'Point of No Return', of black holes. One of the particles formed would be sucked into the black hole, while the other would be shot away thanks to the myriad of forces surrounding a Black Hole. This is what he hypothesized was making the spout out of the Black Holes he was describing.
Although quantum physics doesn't always adhere to the normal Natural Laws that macro-organisms and other bodies have to obey, it is still an important part of nature and helps to drive many of the important mechanisms of Life and the Cosmos at large.