In most cases, yes, a pond pump should run continuously, and pond pumps are built for exactly that. The important thing to understand is that a pond and water feature pump is rated for continuous duty, 24 hours a day, 7 days a week.
Most ordinary submersible drainage or puddle pumps are not: run one of those non-stop and it will overheat and fail early.
Why continuous running is usually best
If your pond has fish or a filter, continuous running is important. Constant circulation keeps oxygen levels up and stops warm, stagnant, oxygen-poor water settling at the bottom. Just as importantly, the beneficial bacteria in a biological filter need a constant flow of oxygenated water; switch the pump off for long periods and those bacteria start to die, which undoes the filtration your pond depends on. Keeping the water moving also keeps it clear and healthy.
When it depends
How long you run the pump does depend on the pond: the type, the fish load, the planting, the weather, and whether it feeds a filter. A stocked, filtered pond generally wants the pump running around the clock, and in hot weather that becomes more important, not less, because oxygen is scarcest then.
A purely ornamental feature with no fish or filter can be run when you want the display, though circulation still helps keep it clean. We give some typical run-time guidance on the pond and water feature pump collection.
The catch: run it in the right place on its curve
If a pump is going to run 24/7, it is worth making sure it runs efficiently, because a pump working flat out in the wrong place on its performance curve wears faster and costs more to run.
The rule we use is to specify a pump so its normal duty point sits in the middle third of its curve, where it is most efficient and component stresses are lowest.
We explain this "middle-third rule" in plain terms, with a car-engine analogy, in our pump guide, and the mechanics in how to read a pump curve. On an APP MH150 or MH250, an optional gate valve lets you fine-tune the flow to sit the pump comfortably mid-curve, which is ideal for a pump that never switches off.
