Many people believe a pump will keep the water crystal clear. A pump will help keep the water clear, but that's all. A pump moves water and provides oxygen for the fish if you feed them and the pond is overpopulated. If you have a natural ecosystem there will be no overpopulation and therefore you will not need any pump if you don't wish to have one. A pump will also ensure that you will never breed mosquitoes. I generally suggest that folks have pumps for that very reason. And now that we have reliable solar pumps, lack of electricity is no longer an excuse. Most folks like them because we all like the sound of moving water and waterfalls.
If you have a waterfall, use a pump that moves each hour at least as many gallons as your pond holds. I use a 4300 gph pump, tee the output into two hoses and have great results. Generally, we leave pumps on 24 hours daily, but no pump has to be turned on all the time unless you feed your fish or have koi. You can set your pump on a timer and have it run only when you are outside to enjoy it. With electricity costs rising these days, a timer, available at most big box home improvement stores, might be just the thing to keep those costs down.