It's been mentioned earlier, but I'll expound on it: the battles of Trebia, Lake Trasimene and Cannae during the Second Punic War.
Trebia - After Hannibal completed the long and treacherous crossing of the Italian Alps, he engaged the Romans at Trebia. The Romans, despite outnumbering the Carthaginians (16-18,000 infantry, +4,000 cavalry and 20,000 auxiliaries compared to Hannibal's 30,000 infantry, 11,000 cavalry and a few elephants) were provoked into a frontal assault and were later encircled by the Carthaginians, a tactic which Hannibal would use to great effect at Lake Trasimene and Cannae. The battle however, set the stage for Cornelius Scipio to eventually take power and defeat Hannibal.
Lake Trasimene - The largest and most successful ambush in history. Carthaginian troops attacked the Roman legions at Lake Trasimene. The Romans, who were not used to fighting out of formation, were slaughtered and pushed back into the lake, where they drowned due to their heavy armor.
Cannae - Rome's second biggest military loss. Rome fielded 86,000 men under the command of two Consuls (Gaius Terentius Varro and Lucius Aemilius Paullus) and were soundly defeated by Hannibal's 56,000 troops. The Romans massed their infantry in deeper formation than normal and charged at Hannibal's "center" (his Gallic auxiliaries). As the Gauls fell into a fighting retreat, the Romans were sucked into the Carthaginian lines, which surrounded them while they were fighting the Gauls. When the Romans were fully surrounded, the Carthaginians simply went and collapsed the Roman lines.