If you have fish in your pond, they will deplete the dissolved oxygen in your pond inside of a couple of hours and suffocate if you do not have a pump or aerator running. You can safely run your pond on a timer if you have a pond oxygen sensor and have established the rate at which your fish stock depletes the dissolved oxygen in the water. For most fish ponds, however, constant aeration by running the pumps will be a requirement.
Algae is the green, goopy, pea-soup-like buildup that you see floating on pond and lake surfaces in summer. Algae is a photosynthetic organism, meaning it uses the sun's rays to make food and possesses requirements similar to plants. If your pond is exposed to more than two hours of direct sunlight per day and is still for substantial amounts of time, you are going to develop an algae problem. Keep your pond pumps running around the clock to prevent water stagnation and unsightly algae buildup.
In nature, ponds strike a balance between decaying organic matter and bacterial growth. This balance allows a pond to self-clean and remain a source of clean water for organisms for miles around. A backyard pond, however, left undisturbed and stagnant, is more akin to a flooded storm drain. The water becomes unsightly, with large amounts of algae buildup and decaying plant matter. If you do not treat your pond with chemicals in much the same way you treat a pool, you must keep your pond pumps running at least 12 hours of every day in order to prevent stagnation and bacterial growth.
If mosquitoes are a problem in your part of the world, as they are in most locations, you are not going to want to leave your pond water still for very long. Mosquitoes can breed and hatch in as little as a teaspoon of water, and your pond will be host to thousands of larvae. Skeeters require still water to breed and lay their eggs, so running your pond pumps around the clock is a good way to make them take a second look at the neighbor's yard when it's breeding time.