Another good article on this:
http://www.catholic.com/library/Apostolic_Succession.asp
Also quotes the Fathers
Thanks for the link! Anything there that you feel would contribute to this thread? Perhaps you can blockquote it.
Here's a snip from the Letter of Pope Celestine to the Holy Fathers assembled for the Council of Ephesus. Its likely it was originally written in Latin but was translated into Greek and read aloud in that language at the Council. It was later translated back into Latin, but the Latin is terrible so the Greek version is usually considered authoritative as the Latin original is lost.
"Every council is holy on account of a peculiar veneration which is its due; for in every such council the reverence which should be paid to that most famous council of the Apostles of which we read is to be had regard to. Never was the Master, whom they had received to preach, lacking to this, but ever was present as Lord and Master; and never were those who taught deserted by their teacher. For he that had sent them was their teacher; he who had commanded what was to be taught, was their teacher; he who affirms that he himself is heard in his Apostles, was their teacher. This duty of preaching has been entrusted to all the Lords priests in common, for by right of inheritance we are bound to undertake this solicitude, whoever of us preach the name of the Lord in divers lands in their stead for he said tothem, Go, teach all nations. You, dearbrethren, should observe that we have received a general command: for he wills that all of us should perform that office, which he thus entrusted in common to all the Apostles. We must needs follow our predecessors. Let us all, then, undertake their labours, since we are the successors in their honour. And we shew forth our diligence in preaching the same doctrines that they taught, beside which, according to the admonition of the Apostle, we are forbidden to add aught. For the office of keeping what is committed to our trust is no less dignified than that of handing it down.
They sowed the seed of the faith. This shall be our care that the coming of our great father of the family, to whom alone assuredly this fulness of the Apostles is assigned, may find fruit uncorrupt and many fold. For the vase of election tells us that it is not sufficient to plant and to water unless God gives the increase. We must strive therefore in common to keep the faith which has come down to us to-day, through the Apostolic Succession. For we are expected to walk according to the Apostle."