The classic example comes all the way from ancient Greece, during the mythological Trojan War (possibly, but probably not based on actual historical events). After an exhausting, unsuccessful 10-year siege of Troy, the Greek army appears to give up. They pack their things, set sail, and leave the Trojans an enormous wooden statue of a noble horse -- an impressive gift to say "We lose. You win. Good game."
The Trojans wheel the horse into the gates, congratulate themselves, eat, drink, and be merry themselves into a sound sleep. Little did they know that hidden inside the horse was a small force of Greek soldiers. The soldiers crept out of their equine hideaway during the night, opened the city gates, and let in the rest of the Greek army, which had quietly returned under dark of night while the Trojans were carousing. The Greeks entirely destroyed the city of Troy, and the Trojans who survived had to live with the knowledge that, after their security measures held strong for 10 years, they'd allowed their own undoing by foolishly inviting their destroyers to come right in.
Mythical or not, if the Trojan Horse weren't such a genius example of a social engineering attack, we'd never have named an entire class of malware after it.
(Image: Mykonos vase (Archaeological Museum of Mykonos, Inv. 2240). Decorated pithos found at Mykonos, Greece depicting one of the earliest known renditions of the Trojan Horse.)