While such factors as corruption and political instability contributed to the fall of Rome, the primary reason for its demise was its size and inability to effectively managed that size. Though many things contributed to the empire's demise, those three things are the biggest factors. All of these 3 things together mixed with a lot of little things, caused the Roman Empire to fall.
Corruption in Rome was widespread, both politically and socially. The rich ruled and the poor had no power. There was no middle class in Rome. Emperors and nobles threw huge, extravagant gladiator parties that were extremely wasteful. Politicians constantly plotted against each other and their own leader. An example of this is when Caesar was assassinated. This is considered by many to be the death of the Roman Republic and the start of the Roman Empire, which began to decline 200 years after Augustus, the first Emperor took the throne.
Political instability came in the form of there being to clear successor each time the emperor died. There was no clear established rule of a particular family, or bloodline. Instead a popular general, someone that the politicians or army picked, or sometimes a relative of the former emperor ruled. Because of this a brief period of anarchy reigned each time an emperor died or was assassinated.
The major reason Rome fell was that its own sheer size worked against it. The actual decline of Rome, in the litteral sense, is thought to have begun with the reign of Commodus in 180A.D. Lanes of communication in military, food supplies, and cultural terms, were far to tortuous. Troops defending a particular point had to be withdrawn to fight another battle on the opposite side of the empire.
Another thing that was instrumental in Rome's fall that...