The Roman Empire had been in decline for centuries by the time Odoacer deposed the child emperor Romulus Augustus in 476 and declared himself ruler of Italy – the first time any non-Roman had done so.
His Italy remained more or less a client state of the Eastern Empire (the portion of the old Roman Empire that would become better known as Byzantium, and last for just under another millennium), and that in itself helps to illustrate the decay of Rome. From the point several centuries earlier at which Roman expansion ceased, to the splitting of the Empire into East and West in 395 after the death of Emperor Theodosius, the signs had been present for some time, and only growing stronger.
Even Odoacer’s sack of Rome was the third in less than seventy years, and when a nation can no longer defend its capital, you know things aren’t going well. Even so, the use of this date as the official Fall of Rome is fairly arbitrary – there are no shortage of other dates that have a just claim to the title.