One must remember that filtration serves more than one function, and these vary considerably according to the tank's biology and the type of fish. Other members have wisely mentioned plants and fish stocking, and they are also part of the equation.
Filtration occurs as mechanical, biological and chemical. Mechanical is moving the water through media (esp floss, pads, sponge, foam) to remove suspended particulate matter. Although it is possible to have planted tanks without mechanical filtration, it is beneficial for most tanks and it also helps circulate the water.
Biological involves encouraging nitrifying bacteria colonization in the filter media. While here too it is not essential, it is advisable (a) if there are no live plants, and (b) if the fish stocking is anything above what the tank can easily handle naturally. Most of us put more fish in a tank than what may be termed "moderate."
Chemical involves adjusting the water chemistry somehow, often with activated carbon and other substances that will remove toxins (ammonia, nitrite, nitrate, metals, etc). This again is not necessary in planted tanks or those with moderate fish stocking that balances the tank's biological system.
A sponge filter will easily achieve mechanical and some biological. Provided the fish stocking is moderate, this is fine. And with live plants, even better.
Another important aspect of filters is the water movement. Some fish need more current than others, and this must be provided or that species will not be healthy. This is another important aspect of selecting "compatible" fish for an aquarium. Compatibility includes similar requirements respecting water flow, temperature, parameters, environment...in addition to behaviours.