Do we know of any family trees that actually are documented all the way from Roman (or classical) antiquity down to modern times? I guess I'm just curious as to any individuals from classical antiquity that we have anything more than spuriously claimed descendants. (I do realize that according to some estimates almost every person from classical antiquity that had children that also had children probably is the ancestor of most Europeans, if not humans.)
Many Europeans (And all European royal houses) can in one way or another trace their ancestry back to Charlemange. There have been many attempts to connect Charlemange to antiquity, but none have been absolutely certain.
As far as Europeans are concerned, the answer to your question is no. After the fall of the Western Roman Empire, there was a period in time where records simply weren't being kept. It took several centuries before Charlemange and others reestablished prominent families, and several more before peasantry began to be recorded (Initially, simply for tax purposes).
Many royal families simply invented more prestigious family trees to make themselves seem more legitimate. So even if you are descended from one, you have to take everything that hasn't been independently varied by historians with a grain of salt.
The problem of a lack of reliable records plagues descent from antiquity, as it is known, in all parts of the world. The Imperial family of Ethiopia claimed descent from King Solomon, for example. However, no records exist from this time. This would hypothetically mean they could trace themselves back to Adam and Eve, as saying they were descended from King Solomon was no more reliable than taking the Bible to be a fully accurate historical record in it's entirety.
It is considered to be at least likely that due to the Chinese being very fond of familiaral record keeping, some people do have accurate records of descent from Confucius.
Old related questions
as one of them points out the Hashamites (Jordanian Kings) sneak in at the end of antiquity.