Yes, there are a number of virtual worlds that focus on animal games such as Adopt Me, Neopets and Switch Zoo. Adopt Me is a free virtual game that allows you to adopt an animal ranging from dogs and cats, to fish and horses. The aim of the game is for you to take care of your pet and play with it regularly. Moreover, you have to play games in order to win points which pay for food for your animal. You can spend the points you earn in the Adopt Me town or take your pet out to play some games for fun. In addition, you can design your pet's home as well as interact with other animals and create a blog for your pet.
Another virtual game is Neopets which is an online world that creates animal like characters including JubJub, Korbat, Scorchio and many more. Once you have chosen one of the animals available, you can give them a name and create their home, as well as get weapons and items for your character. You earn points by playing games and winning daily challenges, in which you can trade for armor or weapons.
Another game that focuses on animals is Switch Zoo in which you can create your own animal by mixing images of a range of different animals. You have a choice of around 142 species so you can make your animal truly unique. Once you've created your animal you can then start building a habitat for them as well as write a story about them.