Basically there are levels of Deities. The higher and lower ones are separated into their specific category, with the capital gods Din, Nayru, Farore, Hylia, Zephos, and Cyclos being the most notable gods, and others such as the Great Deku Tree, The Four Giants, and others being spirits.
Nayru, the Goddess of Wisdom, is one of the three most important deities in the Zelda mythos. She came down from the heaven and created the world and Hyrule along with Din and Farore. She is credited with the creation of the laws of the universe and magic. Like the two other Goddesses, her power is represented in the Triforce. Her Triforce is the left one and her choosen hero is usually Princess Zelda who receive near endless wisdom from her Triforce. Nayru is also often affiliated with water and the Zoras.
Din, the Goddess of Power is one of the three most important deities in the Zelda mythos. She came down from the heaven and created the world and Hyrule along with Nayru and Farore. She is credited with the creation of the land. Like the two other Goddesses, her power is represented in the Triforce. Her Triforce is the top one and her choosen hero is usually Ganondorf, the Gerudo King, who receive near absolute immortality and power from his Triforce. Din is often affiliated with fire and the Gorons.
Farore, the Goddess of Courage is one of the three most important deities in the Zelda mythos. She came down from the heaven and created the world and Hyrule along with Nayru and Din. She is credited with the creation of all life. Like the two other Goddesses, her power is represented in the Triforce. Her Triforce is the right one and her choosen hero is usually Link who receive limiteless courage from his Triforce.
Hylia is the Goddess who was entrusted with the Triforce by the Three Golden Goddesses. She is the namesake for the Hylian race and is heavily worshiped by the Sheikah who were her servant prior to Demise's sealing and Hylia's death. She was later reincarnated into the first Zelda and started the Hyrule Royal Family and the source of their powers. By the time of Breath of the Wild, she seems to have returned to her original state.
Demise is an extremely powerful entity who consider itself as the ruler of the Demon Tribe. Demise is said to be eternal and to have conquered time itself as well as being the source of all monsters in existence. Its appearance is mearly an illusion that change depending on who lays eyes on it. It is strong enough to kill Hylia's physical form during their first fight and forced her to become a human for some times. He was originally sealed at the end of the war between Hylia and itself. His physical form was eventually defeated by Link with the Master Sword but as a being that conquered time itself, Demise found a way to retain his influence over the world by having its hatred for Link and Zelda become Ganon. Demise is also the reason why Link, Zelda and Ganondorf are forced to be reincarnated across the ages.
Ganon is the manifestation of Demise's undying hatred. Ganon generally manifest itself as Ganondorf's most powerful form or by itself when a humanoid vessel is not needed. Like Demise, Ganon is worshiped by the Demon Tribe as a god and has the power of one. In Breath of the Wild it is also said that the Yiga Clan are Sheikah who abandoned Hylia for Ganon.
Malanya is the Horse God. Like his name suggest, he take care of anything related to horses in the Zelda universe and even have the power to bring them back to life if the met an unfortunate end. Malanya looks like a giant humanoid made of wood with a horse head and disembodied hands.
Cyclos and Zephos
Cyclos and Zephos are two brothers that serves as the gods of wind. In The Legend of Zelda: The Wind Waker, it is shown that after being angered by the destruction of his shrine, Cyclos created giant cyclones all over the Great Sea. They seems to be revered by the Ritos as their shrines are on Dragon Roost Island. They appears as giant frogs sitting on clouds.
The Fierce Deity
The Fierce Deity is an extremely destructive Deity sealed inside the Fierce Deity's Mask in The Legend of Zelda: Majora's Mask. Almost nothing is known about the Fierce Diety except that it is an extremely violent deity that is refered as the "True Bad Guy" by the spirit sealed inside the Majora's Mask, which can either mean that the two were ennemies or that even a world ending threat like Majora believe that the Fierce Diety is worse than him.
Lord Jabu-Jabu is a large whale like creature that serves as the guardian spirit of the Zora tribe during The Legend of Zelda: Ocarina of Time and The Legend of Zelda: Oracle of Ages. He is a very benevolent guardian deity and the Zoras usually encourage outsiders to encounter the spirit even if they are not Zora themselves.
Great Deku Tree
The Great Deku Tree is a giant tree-like spirit that serves as the guardian deity of the Kokiris even when they eventually became the Koroks. He is usually found at the center of a huge forest where he lives alongside the Kokiri/Koroks and act as the protector of the forest. During the Great Flood, the Great Deku Tree was mainly known for his attempt to reclaim some land from the depths of the Great Sea overtime using seeds to great new trees that would eventually consolidate the groundnear the coasts of most islands. He is also the protector of the Master Sword, a divine weapon created by the Goddess Hylia, in Breath of the Wild.
Valoo is a dragon-like spirit that serves as the guardian deity of the Rito. During The Wind Waker, the Ritos are not able to grow their wings by themselves so they must ask Valoo for one of his scale, which contains the power of the guardian spirit and makes their wings grow. He is also seen activelly combating Ganondorf during The Wind Waker, which may indicate that Valoo may sometime leave his island to fight evil himself.