Like the Romans, the Incas permitted the cultures they integrated into their empire to keep their individual religions. Below are some of the various gods worshiped by the peoples of the Incan empire, many of which have overlapping responsibilities and domains. Unless otherwise noted, it can safely be assumed these were worshipped by different ayllus or worshipped in particular former states.

Apo or Apu was a god or spirit of mountains. All of the important mountains have their own Apu, and some of them receive sacrifices to bring out certain aspects of their being. Some rocks and caves also are credited as having their own apu.
Apocatequil (aka Apotequil) or Illapa was the god of lightning.
Ataguchu was a god who assisted in creation myth
Catequil was a god of thunder and lightning
Cavillace was a virgin goddess who ate a fruit, which was actually the sperm of Coniraya, the moon god. When she gave birth to a son, she demanded that the father step forward. No one did, so she put the baby on the ground and it crawled towards Coniraya. She was ashamed because of Coniraya's low stature among the gods, and ran to the coast of Peru, where she changed herself and her son into rocks.
Chasca was the goddess of dawn and twilight, and Venus. She protected virgin girls.
Chasca Coyllur was the goddess of flowers,young maidens, and sex.
Kuka Mama or Mama Kuka (in quechua: Mother coca) was a goddess of health and joy. She was originally a promiscuous woman who was cut in half by her many lovers. Her body grew into the first coca plant, the leaves of which men were only allowed to chew (to bring health and happiness) after having given a woman an orgasm.
Coniraya was the deity of the moon who fashioned his sperm into a fruit, which Cavillaca then ate. When she gave birth to a son, she demanded that the father step forward. No one did, so she put the baby on the ground and it crawled towards Coniraya. She was ashamed because of Coniraya's low stature among the gods, and ran to the coast of Peru, where she changed herself and her son into rock huacas.
Copacati was a lake goddess.
Ekkeko was a god of the hearth and wealth. The ancients made dolls that represented him and placed a miniature version of their desires onto the doll; this was believed to caused the user to receive what he desired.
Illapa ("thunder and lightning"; aka Apu Illapu, Ilyap'a, Katoylla) was a very popular weather god. His holiday was on July 25. He was said to keep the Milky Way in a jug and use it to create rain. He appeared as a man in shining clothes, carrying a club (weapon) and stones. He was formerly the main god of the Kingdom of Colla after which the Collasuyu province of the Inca empire was named.
Inti was the sun god. Source of warmth and light and a protector of the people. Inti was considered the most important god. The Inca Emperors were believed to be the lineal descendants of the sun god.
Kon was the god of rain and wind that came from the south. He was a son of Inti and Mama Quilla.
Mama Allpa was a fertility goddess depicted with multiple breasts.
Mama Cocha ("sea mother") was the sea and fish goddess, protectress of sailors and fishermen. In one legend she mothered Inti and Mama Quilla with Viracocha.
Mama Pacha (aka Pachamama) was the wife of Pachacamac and a dragoness fertility deity who presided over planting and harvesting. She caused earthquakes.
Mama Quilla ("mother moon" or "golden mother") was a marriage, festival and moon goddess and daughter of Viracocha and Mama Cocha, as well as wife and sister of Inti. She was the mother of Manco Capac, Pachacamac, Kon and Mama Ocllo.
Mama Zara ("grain mother", aka Zaramama) was the goddess of grain. She was associated with maize that grew in multiples or were similarly strange. These strange plants were sometimes dressed as dolls of Mama Zara. She was also associated with willow trees.
Pacha Camac ("Earth-maker") was a chthonic creator god, earlier worshiped by the Ichma but later adopted into the creation myth of the Inca.
Pariacaca was a god of water in pre-Inca mythology that was adopted by the Inca. He was a god of rainstorms and a creator-god. He was born a falcon but later became human.
Paricia was a god who sent a flood to kill humans who did not respect him adequately. Possibly another name for Pachacamac.
Supay was both the god of death and ruler of the Uca Pacha as well as a race of demons.
Urcaguary was the god of metals, jewels and other underground items of great value.
Urcuchillay was a deity that watched over animals.
Viracocha was the god of everything. In the beginning he was the main god, but when Pachacutec became Inca, he changed this god's importance pointing out that it was Inti who allowed him to defeat the chancas (The Incas' main enemies at that time).