Battle of Cannae
Fought between Carthage and Rome in 216 BC, the Carthaginian commander, Hannibal, decisively defeated Roman forces under Lucius Aemilius Paullus and Gaius Terentius Varro. Even though it was a major Carthaginian victory, it did not reverse the war and Rome eventually won.
Classic tactical example
This battle is often taught as the best example of the tactic of double envelopment.