August 19, 1071 - Battle of Manzikert:

Here is a short article by Austin Clie about the battle that marks Turkish people's entry to Anatolia, from About.com:

Alp Arslan leads an army of Seljuk Turks against the Byzantine Empire near Lake Van. Numbering perhaps as many as 100,000 men, the Turks take the fortresses of Akhlat and Manzikert before Byzantine Emperor Romanus IV Diogenes can respond. Although Diogenes is able to recapture Akhlat, the siege of Manzikert fails when a Turkish relief force arrives and Andronicus Ducas, an enemy of Romanus Diogenes, refuses to obey orders to fight. Diogenes himself is captured and released, but he would be murdered after his return to Constantinople. Partly because of the defeat at Manzikert and partly due to the civil wars following the murder of Diogenes, Asia Minor would be left open to Turkish invasion.