Historians do not agree on a single cause for the fall of Rome. Instead, many factors, including barbarian aggression, divisions within the Empire, government corruption and a change in values and culture caused the Empire's downfall.
The Roman Empire expanded greatly in its last centuries, leading to more interactions with barbarians. While some barbarians were incorporated into Rome's military, increasing barbarian attacks weakened Rome to the point that the Western Empire crumbled.
In the third century, Rome was divided into two separate empires, Western and Eastern Rome. The Eastern Empire grew to be the most powerful of the two and held on long after the Western Empire fell apart. Eastern Rome was still a major power until the 1400s.
The size of the Empire led to government corruption becoming a larger issue, due to how difficult it was to keep all of the sections of the Empire in working order. Internal fighting led to a constantly changing leadership that resulted in a lack of trust from the population.
The addition of barbarians and Christianity to the Empire drastically changed Roman culture. Values and way of life, as well as the process of government, all changed as church officials became the power players of the time.