Explanation: Due to Rome's longevity and its wide reach, there are a number of dates that can be used as its fall - some quite, uh, interesting. For bonus points, my date of choice isn't here.
Oh, and for those curious, the most commonly accepted answers are:
476 AD (Fall of the city of Rome and the Western Empire)
1204 AD (Sack of Constantinople and the break of government continuity in the Byzantine Empire)
1453 AD (Siege of Constantinople and conquest of the Byzantine Empire by the Ottoman Turks)
476 is less arbitrary than most, but still not really satisfactory. 1204 has a strong claim by pure logic, but logic doesn't always run historical narrative. 1453 is the most dramatic answer, but needs some wiggling to get to.