Water changes are necessary regardless of wether or not the tank looks clean, because what you need to be removing is the ammonia. Ammonia has no scent, color, or taste, but it burns gills and helps the water become breeding grounds for nasty bacteria and pathogens which can cause finrot or other problems. Ammonia is created by your fishs' excretements (poo and what not), in any food left in the tank, even when he or she exhales. It slowly builds up and the only way to remove it is by doing a water change and replacing the water with clean water.
With a two gallon, I recommend at least a 100% water change once a week. Be sure to scrub the sides down with hot water when possible. :)