The problem with most games on Android is a distinct lack of cute. This is no problem for Pet Rescue Saga, which just arrived on Android and is positively overflowing with puppies and kittens. I think there are some puzzles in there too.
Pet Rescue Saga is a casual puzzler that ties in with Facebook. In fact, the game has over 10 million players on the Facebook app. The game affords you the opportunity to solve block-based puzzles and compete against your friends.
The graphics are clean and simple, with ample small furry animals. Pet Rescue Saga is free, but gives only a limited number of lives. You either have to interact (bother) with friends to earn more, or buy them through an in-app purchase. If you aren't cool with plugging in your Facebook info and playing against friends, there are better puzzle games out there. But... puppies.