As the saying goes, "Rome wasn't built in a day," and neither did the Roman Empire fall in a day. There are a number of reasons for the collapse of the Roman Empire — a decline that took place over many hundreds of years. The rise of Christianity did play a small, but not insignificant, part in the decline, in that it eroded traditional Roman beliefs and values and caused conflicts between Christians and those who continued to hold onto the old pagan philosophies. These conflicts led to persecution of the Christians, until the first Christian Emperor of Rome, Constantine, put a stop to the persecution.
Most historians believe that there is a long list of causes for the fall of the Roman Empire. The internal causes included political corruption, economic problems, and a series of leaders that — let's face it — were more interested in their personal gain than in the welfare of the common people. The external causes ranged from disease and plagues that ravaged the population, to attacks and defeats from the Germans, Huns, and various barbarian tribes that weakened the Roman military and vastly decreased the amount of territory controlled by the Empire.
By 286 AD, the Empire was a mere shell of itself, and the Emperor Diocletian split the Empire into two: East and West. The Eastern Empire would eventually become the Byzantine Empire, while the Western Empire would decline into nonexistence. By 476 AD, the remnants of Roman Empire were finally destroyed, after barbarian tribes removed the last Roman Emperor, Romulus Augustus, from power and Roman rule over Europe was no more.