Hindus do not worship animals, although it is believed that the spark of the divine, the soul, is present in animals.
There are idols that have animal features. Lord Ganesha is a young boy who has the head of an elephant, after his father (God Shiva) cut his head off for disobeying him. He is called Lord Vighneshwara, and is leader of the celestial army, the Ganas. He also grants auspiciousness.
There is Lord Hanuman, a vanara, (an extinct race of intelligent monkeys) who is worshipped as the ideal deovtee, and is an immortal who was given the promise by God Rama that where ever the story of Rama is told, Hanuman may be present.
It is commonly mistaken that monkeys are worshipped; this is not so, Lord Hanuman is worshipped as a model devotee of the Divine.