About a week or so ago, I spent $0.99 at iTunes to pick up a copy of Koi Pond. With all the software that constantly moves onto and off of my iPhone, it should say something that over a week later, Koi Pond is still installed. It's a little treasure.
Koi Pond provides exactly the experience its title suggests: it puts a virtual Koi Pond onto your iPhone, allowing you to place plants and feed the fish. The fish in question swim around the screen and run away from the rippled waves you create when messing with the water. If you leave your finger still enough, eventually a koi or two will investigate and nibble on your finger before darting off on its pre-existing fishy business.
In theory, there is no point to Koi Pond. It's there to experience and enjoy. In practice, my elder children issue each other challenges: "Make the worst pond" (no fish, no plants, no sunlight, brown rocks, rotting food) or "Make the most psychotic koi" (one fish, sunlight, lots of splashing), etc.
For $0.99, it's a great deal on a little toy. Turn off autolock and cheerfully burn out your screen by sitting it on a stand on your desk. The fish will swim and burble ad infinitum. (It helps to have the iPhone docked while doing this.)
Koi Pond is available for iPhone and iPod touch. It costs $0.99 at the iPhone App Store.