I’ve been receiving email about this:
Meet Prince Lorenzo Borghese, the new ‘Bachelor’
According to this article, Prince Lorenzo Borghese “is the son of Prince Francesco and Princess Amanda Borghese… His paternal ancestors include Pope Paul V (Camillo Borghese) and Cardinal Scipione Borghese.”
He does not appear to be a member of the former Italian royal family.
Wikipedia has more info on the Borghese family.
You can read about Italian titles of nobility here.
For news, books, and links about Italy’s former royal family, see Royalty.nu’s Italian Royalty page.
UPDATE: To clarify, he is really a prince, but this is a title of nobility, not a royal title. The links above will help explain his title and family background.