Guppies are hardy fish and it is possible to keep them in an unfiltered tank without a pump, as stated by FishChannel. However, unfiltered tanks are complex projects best reserved for advanced fish keepers.
Guppies have been known to survive months stored in water bags without the water being refreshed, notes the International Guppy Education and Exhibition Society. However, this is an extreme circumstance usually caused by the fish owner forgetting that he or she packed the guppy for shipping. In addition, the guppy bag had extra air in the top and a mild sedative or water oxygenator was added to the water before packing. Basically, the guppies were prepared for long storage.
Very experienced fish owners may experiment with unfiltered tanks that do not have an air pump. However, it is a difficult task maintaining the health of the fish with just the right balance of filtering plants, aquatic life and daily water changes. Despite the stories of guppies surviving without air pumps, the average fish owner should ensure that a guppy tank is fitted with an appropriate pump. When living in a tank, guppies swim freely, excrete waste and use a lot of oxygen. An air pump helps force oxygen back into the water continuously, pushing tiny air bubbles into it.