As told by Aeschylus, Ovid, The Homeric Hymns, Bacchylides, Hesiod, and who knows how many others.
The condensed-but-still-really-long version: Zeus was picnicking with one of his girlfriends (Princess Io of Crete) until his wife Hera found out about it, at which point Zeus turned Io into a cow so Hera wouldn’t be suspicious. Sadly, cows aren’t the most inconspicuous of animals so Hera took the cow anyways, and made one of her servants, a monster called Argos Panoptes, watch over it day and night.
Argos was a giant with 100 eyes all over his body (yes, very disturbing), which made him very hard to kill because as soon as some eyes closed, others would open, so Zeus had employ Hermes’ help. Hermes, being the B.A.M.F. that he is, devised a way to lull Argos to sleep. Some say he played lullabies on his pipes, while others say he simply bored Argus to death by talking too much.
Anyhow, after all of Argos’ eyes closed, Hermes sliced off his head (don’t worry - Hermes isn’t usually this homicidal) and freed Io. This is why Hermes is sometimes called Argeiphontes, which means “Argus-slayer”.
But then Hera sent a gadfly to torment Io and drive her away into Egypt, and apparently Hermes couldn’t be bothered with saving her again, so Io ran all the way across a sea (afterwards named the Ionian Sea in her honour), trying to evade the fly. When Io got to Egypt, Zeus finally took pity on her and turned her back into a human, whereupon the Egyptians began worshipping her as a queen :D
Also, in gratitude of Argos’ loyal service to her, Hera took all 100 of his eyes and put them on her sacred bird, the peacock, which is why peacock tails look like they have eyes on them.