After the collapse of the Western Roman Empire, what became of the Roman citizens? Did they remain in Italy, or did they to some other places? Could we say that no "true" ethnic Romans exist today, and are just diluted with other ethnicities?
So I've actually answered variations of this question today, but for Britain, France, Italy and Spain as opposed to the Romans in general. But frankly I think that already covers most of the european western empire.
http://my.reddit.com/r/AskHistorians/comments/2khl6u/where_did_the_goths_go/clm3047
But a basic summary, "ethnicities" are fluid and situational constructs, although there are of course barriers when there is advantage to be had in obtaining an elite identity. As formerly elite identities cease possessing power, identities shift toward alternate elite identities. This is the case for the Romans, as well as their replacements.
Claims about the universality of "blood" or "genetic" identity are really just social constructions built to legitimize ideas about "nations" as essentialist identities stretching across time. In reality, they are invented traditions.
The Romans were more of a culture than a race or ethnicity, but people have said that here already. Many people had already, basically, "given up" on the empire. Honorious (and by that I mean his court, the emperor was a puppet at this point) couldn't send troops to Britannia. People stoped paying taxes to the Romans, tried to defend themselves. The Vandals didn't receive nearly as much push back as they would have generations before when they took over North Africa.
There was still a Roman Empire in the East, but people have up on being saved eventually. And, like bitparity has expertly pointed out: ethnicity is fluid, and you eventually coalesce into the "dominant" culture. That's how the Romans won their empire, in a way: they were the best around at doing exactly that. And now it worked against them.
People would still be "Roman" for a while, and possibly remember their heritage when Justinian came knocking, but sometimes it's best to identify with your neighbors rather than an empire your grandfather told you he was a part of.