I think there are two different dates to consider:
1. Early-Mid 5th century (depending on which date you wish to use): Rome is continuously sacked, and is no longer viewed as a central/important city in the Empire (regardless of the fact that Constantinople was the 'capital'). To me this is the end of Rome, but not of the 'Roman Empire'
2. 1453 CE: Constantinople is sacked, end of the Roman Empire and Byzantine Empire.
I tend to use 410 for #1 above, with the sack of Rome...for me, this is the beginning of the very last chapter of Rome (the city) as a 'great city'. After continuous sacking, rampaging, etc., the city of Rome is quite disorderly and chaotic, and one can see the beginning of the 'Dark Ages' or 'Medieval' period in the 5th century. Certainly for my research, this makes sense; after the Roman centralizing stability has faded into the proverbial sunset, Western and Central Europe move away from the traditional Roman way of life into one which resembles a hodge-podge of Roman, Germanic, and 'native' culture, government, and the like. The Christian Church (can we call it Catholic by this point?) becomes the 'beacon of light' (even if it's a self-placed moniker) for the local communities, and what is considered to be feudal state starts to take root. To be sure, much of this could be placed during the decline of the (Western) Empire, but the 5th century is a crucial time.
However, as others have stated above, this does not diminish the next 1000 or so of the Roman Empire; it simply means that Western and Central Europe were not part of the Empire.