A free program for Android, by Talking Pet.

Dragons are mysterious, magical creatures that roam the world in search of food and water. While they are usually friendly, there is also the chance that they will attack you. You can find them in the wild, or in the human world. If you are lucky, you will be able to find a dragon in your neighborhood. Your goal is to get to know all about dragons and to be able to control them. You need to feed them, play with them and take care of them. 

If you are a beginner, there is a basic tutorial that will help you understand how the game works.