The above answer is both inconsistent and inaccurate. Historians almost unversially accept 476 C.E., the forced abdication of Romulus II Augustulus as the end of the Western Roman Empire. There was no further Western Roman Emperor, and although the Empire itself continued in the East, the Eastern Empire alone survived.
There is no magic to the name of Romulus II Augustulus. He was a feeble minded teenaged boy placed on the throne as a puppet by his father, a Roman general. He was named for the first mythical ruler, Romulus, (hence Romulus II) but Augustulus simply meant "little Augustus." Since the time of Caesar Augustus, the chief Emperor was known as the "Augustus," his heir apparent and second in command as the "Caesar." There was no symbolism, real or imagined, in his name.
With the forced abdication of Romulus II Augustulus, Odoacher forwarded the royal purple robe and scepter to the Emperor in Constantinople together with a message that he (the Eastern Emperor) was now the only Roman Emperor. There was no "huge event," however all events in history need some specific instance to mark important milestones. The milestone marking the end of the Western Roman Empire is 476 C.E. There is no great disagreement among scholars other than by those who wish to prolong needless arguments. Also, even an empire entering a "slow decline" must end at some point. For the Western Roman Empire, that end was unquestionably and absolutely 476 C.E.
I love how you use the word, "really." As your question suggests the date of 476 AD as the fall of the Roman Empire is suspect and open to debate.
Some scholars see 476 as the end of the Roman Empire of the West when Romulus Augustus is deposed by Odoacer. There is something attractive about this date, because Romulus and Augustus are two central figures in the foundations stories of Rome. Romulus was the founder of Rome and Augustus the founder of the Empire. So, the deposition of Romulus Augustus seems fitting as the fall of Rome. However, not all scholars agree for many reasons.
First, the date is somewhat arbitrary. the decline in Rome was very gradual. Hence, to pick one date over another date is not very sophisticated and does not account for the slow decline. There was no one huge event that put an end to everything in 476 A.D.
Second, there was always the East. They were Romans! They would not see the end of the West as an end to Rome.
Third, those who took over saw themselves as Romans, that is, those who kept the traditions of Rome. For example, the Ostrogoths were Romanized and saw themselves as such.