If you prefer your flapping animals to have gills rather than feathers, FlappyFish is worth a look. The graphics are even less impressive than the ones in Flappy Bird (basic but with a certain charm), but the gameplay follows the same principles: place some carefully judged taps on the screen to guide your character safely through the waters and the on-rushing obstacles, which are a little bit too close to each other for our liking.
The difference is you tap to lower the fish from the surface of the water, and you won't get penalised for hitting the top of the screen. Another game where you can expect to see a lot of ads. Available for free for Android and Windows Phone.