Zeus became king of the gods and absolute ruler of the cosmos when he overthrew his father Cronus in the Titanomachy.
I wonder if his reign was ever challenged after that?
In the Illiad, Hera rebels against Zeus, and gets the other gods to bind him to his throne after she drugs him:
"You [Thetis] said you only among the immortals beat aside shameful destruction from Kronos' son [Zeus] the dark-misted, that time when all the other Olympian gods sought to bind him, Hera and Poseidon and Pallas Athene. Then you, goddess, went and set him free from his shackles, summoning in speed the creature of the hundred hands to tall Olympos, that creature the gods name Briareos, but all men Aigaios' son, but he is far greater in strength than his father. He rejoicing in the glory of it sat down by Kronion, and the rest of the blessed gods were frightened and gave up binding him."
I found this on Theoi.com, which also quotes the Argonautica on how Zeus hung his wife in the sky by her hair, with anvils attached to her feet, as punishment.
Typhon, a serpentine giant, attempted to overthrow Zeus. The earliest account of their battle can be found in the Theogony, and according to Hesiod Typhon "would have come to reign over mortals and immortals, had not the father of men and gods been quick to perceive it":
But when Zeus had driven the Titans from heaven, huge Earth bore her youngest child Typhoeus of the love of Tartarus, by the aid of golden Aphrodite. Strength was with his hands in all that he did and the feet of the strong god were untiring. From his shoulders grew a hundred heads of a snake, a fearful dragon, with dark, flickering tongues, and from under the brows of his eyes in his marvellous heads flashed fire, and fire burned from his heads as he glared.
And there were voices in all his dreadful heads which uttered every kind of sound unspeakable; for at one time they made sounds such that the gods understood, but at another, the noise of a bull bellowing aloud in proud ungovernable fury; and at another, the sound of a lion, relentless of heart; and at another, sounds like whelps, wonderful to hear; and again, at another, he would hiss, so that the high mountains re-echoed.
And truly a thing past help would have happened on that day, and he would have come to reign over mortals and immortals, had not the father of men and gods been quick to perceive it. But he thundered hard and mightily: and the earth around resounded terribly and the wide heaven above, and the sea and Ocean's streams and the nether parts of the earth. Great Olympus reeled beneath the divine feet of the king as he arose and earth groaned thereat.
And through the two of them heat took hold on the dark-blue sea, through the thunder and lightning, and through the fire from the monster, and the scorching winds and blazing thunderbolt. The whole earth seethed, and sky and sea: and the long waves raged along the beaches round and about at the rush of the deathless gods: and there arose an endless shaking. Hades trembled where he rules over the dead below, and the Titans under Tartarus who live with Cronos, because of the unending clamor and the fearful strife.
So when Zeus had raised up his might and seized his arms, thunder and lightning and lurid thunderbolt, he leaped from Olympus and struck him, and burned all the marvellous heads of the monster about him. But when Zeus had conquered him and lashed him with strokes, Typhoeus was hurled down, a maimed wreck, so that the huge earth groaned. And flame shot forth from the thunderstricken lord in the dim rugged glens of the mount, when he was smitten.
A great part of huge earth was scorched by the terrible vapor and melted as tin melts when heated by men's art in channelled crucibles; or as iron, which is hardest of all things, is shortened by glowing fire in mountain glens and melts in the divine earth through the strength of Hephaestus.Even so, then, the earth melted in the glow of the blazing fire. And in the bitterness of his anger Zeus cast him into wide Tartarus.
Source: Hesiod. The Homeric Hymns and Homerica with an English Translation by Hugh G. Evelyn-White. Theogony. Cambridge, MA.,Harvard University Press; London, William Heinemann Ltd. 1914.
Interestingly, although Typhon's revolt threatened not only Zeus but all Olympians, this was a fight the thunder god fought alone. Not only didn't the rest of the gods stand by their leader, but - at least according to Pindar and Pseudo-Apollodorus - they transformed into animals and fled to Egypt to escape the battle.
You may find more information on Typhon on theoi.com: