The Hindu deities with non-human animal features include (roughly in order of more to less well known):
- Ganesha
- Hanuman, a Vanara deity. Vanaras are a race of monkeys of human-like intelligence.
- Matsya Avatara
- Kurma Avatara
- Varaha Avatara
- The Goddess Varahi
- Narasingha
- Pratyangira
- Bagalamukhi. Her name means “crane-faced”, and she is traditionally said to have a crane’s head, though most art of her does not show this, in part because her true form is considered too dangerous to look upon.
- Hayagriva
- Surya once took a horse-headed form, often mistaken for Hayagriva.
- Nandikeshwara the bull or half-bull half-man
- Garuda the Suparna (a bird deity, somewhat resembling an eagle or vulture)
- Kamadhenu aka Surabhi, a Cow Goddess, sometimes with a human head with cow horns, human breasts, and/or wings.
- All Naga deities, like Adi Shesha, Manasa, Janguli, Vasuki, Takshaka, and many others.
- Shiva’s Sharabha Avatara, an eight-legged lion-bird creature.
- Shiva and Parvati’s stag and deer forms at Pashupatinath.
- Shiva’s Vrishabha Avatara.
- Shiva has an Avatara that is a pig-headed woman with six breasts, described in Thiruvilayadal Puranam, the Tamil Sthala Purana of Madurai’s Meenakshi Temple.
- Bhairava is depicted in some images as having the face of a dog.
- Vindhyavasini, who has the head of an owl-like bird.
- Kakachandeshwari, a secret crow-headed Goddess of Tantrik alchemy.
- Sarama the Dog Goddess.
- Mallanna, a Sheepdog God worshipped by Hindu shepherds in parts of rural South India.
- Uchchaihshravas, a horse deity.
- Paravani the peacock, mount of Kartikeya
- Many tribal peoples in India worship a tiger god, like Bagh Deo of the Gond tribe, Chitan Deo of the Murias, Bhageshwar of the Bharias, Sonaray of lower Assam (considered by some to be a manifestation of Lord Shiva), Dakshin Rai of the Sundarbans, and many more.
- Very similar to these is Budhi Pallien, a wise yet fearsome and strong goddess of forests and jungles is said to roam northern India, especially Assam, in the form of a tigress.
- Chelamma, a Scorpion Goddess worshipped in southern Karnataka.
- There is a Spider Goddess worshipped in a certain temple, the Palliyara Sree Bhagavathy Temple, also known as the Chilanthi Ambalam in Kerala.
- Naigamesha, who has become obscure and almost forgotten today by most Hindus.
- A mermaid goddess worshipped in Kerala.
I’m sure I’m forgetting some, there are so many.
Edit: Indeed I was forgetting some. Adding a few that commenters reminded me of:
- The twin Ashvin Devas are often horse headed.
- Vishnu’s form Gandaberunda was a great two-headed bird of prey. There is also an eight-headed version.
- Vishnu took the Hansa Avatar, as a swan/goose.
- Vishwaksena, also known as Senai Mudalvar and Senadhipathi, commander-in-chief of Lord Vishnu’s army, is sometimes elephant-headed.
- The deity personifications of the four Vedas are all animal-headed, and two of their female Shakti counterparts are also animal or part-animal. Rigveda is donkey-headed and Rigveda Shakti is a peahen, Yajurveda is goat-headed, Samaveda is horse-headed, Atharvaveda is monkey-headed, and Atharvaveda Shakti has the head of a pig.
- Vishnu’s Navagunjara form combines features of nine different animals: rooster, elephant, tiger, deer, human, peacock, bull, lion, and snake (sometimes horse instead of deer).
And also, I just remembered that Saranyu Devi and Surya Deva took the form of horses and had sex, producing the Ashwinau twins. So those are more animal forms of deities.