The official lineage of Queen Elizabeth takes her back to some Vikings in the 800s.

There are also individuals from whom she is directly descended that claim descent from Odin, which is perhaps less verifiable.

I believe that there are some noble families in Continental Europe that claim descent from Roman nobility (which is sort of the ultimate prize as a noble) but I recall that those claims were even more tenuous than most.

edit: this thread might be interesting http://www.reddit.com/r/AskHistorians/comments/12lghm/whats_the_longest_traceable_historical_lineage/ . It says that I'm wrong: maternally, Elizabeth II can be traced back to the 500s. A wikipedia link also points to http://en.wikipedia.org/wiki/Niall_of_the_Nine_Hostages as the longest European family tree, with the Confucius family tree and the http://en.wikipedia.org/wiki/Lurie family tree being the other two worthy of note.

The Hashemite clan can trace directly back all the way to the great grandfather of Muhammad Ibn Abdullah who himself was born in the late 6th century. So that genealogy goes back to at least the the early 6th century if not into even the 400s.

What makes their lineage easier to discern and verify than most is the fact that patrilineal bloodlines are such a huge aspect of Arab culture, as it always has been. Extensive catalogues of lineage were recorded and preserved. Even lesser families in the Arab world tend to have family trees going back centuries.

So there's a candidate.

The Duke of Yansheng is a title that was given to the direct main line descendant of Confucius. The title was changed to Sacrificial Official to Confucius in 1935 and that office still exists in Taiwan. The current holder is Kung Tsui-chang who is the 79th generation descendant. So their genealogy can be traced back to the 5th century BCE.