Pond pumps keep the water in a pond from becoming stagnant and help discourage the growth of algae. Additionally, pumps oxygenate the water, which is important if you hope to keep fish in your pond. Whether or not your small pond needs a pump depends on a few factors.
Keeping fish in a pond without a pump is a recipe for disaster. Pond fish depend on pumps both to filter their excrement from the water and to keep the level of dissolved oxygen in the pond water at a suitable level. Fish may live for a short time in a small pond without a pump, but will quickly run in to problems unless the water is frequently changed.
Pond plants can help keep your pond water clean in the absence of a pump in a few ways. First, they filter out dissolved nutrients in the water while competing with algae. All of the nutrients being absorbed by the plants is nutrients not available for the algae, and they help prevent the dreaded "pea soup" of algae overgrowth. Additionally, they help shade the pond and reduce the amount of sunlight reaching the water, further inhibiting algae growth.
The amount of sun your pond gets will also determine how well it will fare without a pump. A pond that gets a lot of direct sun will almost certain suffer from algae overgrowth in the absence of a pump and some kind of filtration system. Placing your pond in a shaded area without placing it under a tree that will drop leaf litter can be a difficult task, so using a garden umbrella or awning may be helpful.
Alternative Methods of Cleaning
You may choose to use barley straw in an old stocking or sock to help prevent algae. Or, you can use a commercial product designed to inhibit algae growth and keep your water clean. You can also manually clean your pond using a strainer or small plastic rake. Note that a pond without a pump may also become a breeding ground for mosquitoes, so consider it carefully, especially if you live in an area with West Nile virus.