You have asked a question that is very wide open, because there are some very tiny animals among the invertebrate species (insects, corals, roundowrms, etc.). I think you were probably hoping for vertebrate animal answers however.
Among mammals, the pygmy shrew (Suncus erruscus) and the Kitti's hog-nosed bat (Craseonycteris thong longyai) are the smallest, at 1.5 and 1.6 grams respectively. The smallest bird is the Bee hummingbird (Mellisuga helenea), which weighs in at 1.6 grams and is easily mistaken for a bumblebee when in flight. The Dwarf pygmy goby (Trimmatam nanus), at 1.5 grams, is the smallest fish.
So far the smallest animal in the world is the amoeba. Amoeba are unicelluar organisms, menaing they are comprised of only one cell and are classed in the animal kingdom under Protozoa. However, some say that the amoeba are not considered as animals, but animal-like protists.
The smallest animal in world, so far, is the Megaphragma caribea, or fairyfly. IT has been found to be 0.10 to 0.17 mm in length. It is an insect. If you wanted to know other types of animals (e.g. with a vertebrae, etc.), look at the link below.