Francis Beckwith has a great article on Apostolic Succession. I encourage you all to read it. While I am less frequently running into non-Catholics who are willing to challenge this point, I am running into more Catholics who bring it into question. I am told, though I don't have the specifics, that there are a couple of books out which tout themselves as scholarly work which try to refute Apostolic Succession. My understanding from others is that these books are persuading to those who are now well grounded in Church history. Let's get the truth out there!