Or: A trip throught Wikipedia lists (always the best part of Wikipedia), wherein I mention a lot of important people that you have never heard of, and that neither your nor I ever hear about. The traditional list of the Patriarchs of Constantinople, going back to Andrew. Wikipedia is a good source for the traditional list of the Patriarchs of Rome, going back to Peter. It also is a good source for the traditional list of the Patriarchs of Alexandria up to Chalcedon, which begins with Mark, and the continuing lists after the Miaphysite split betweem the conciliar (Chalcedonian) Patriarchs of Alexandria and the nonconciliar Coptic Popes. You should also see the traditional list for the Patriarchs of Antioch, also tracing back to Peter, and the split list after 518 between the Patriarchs of Antioch and the Syriac Patriarchs of Antioch. The final element in the Pentarchy is Jerusalem. Its traditional list traces back to James; and you can find the lists of Patriarchs of Jerusalem The current bishops in these seats are, of course: Benedict XVI (Rome), Bartholomew I (New Rome), Theodore II (Alexandria), Shenouda III (Coptic Alexandria), Ignatius IV (Antioch), Ignatius Zakka I (Syriac Antioch), and Theophilus III (Jerusalem). There are also, of course, Latin Patriarchates in the Eastern branches of the Catholic Church, which are responsible to the Pope in matters of faith and morals but are autonomous in everything else: Jerusalem (currently Michael Sabbah), Coptic Catholic Alexandria (currently Stephanos II), Syrian Catholic Antioch (currently Ignace Pierre VIII), Melkite Catholic Antioch (currently Gregory III), Maronite Antioch (currently Nasrallah Sfeir), Chaldaean Babylon (currently Emmanuel III Delly), and Armenian Catholic (currently Nerses Bedros XIX).
The Chaldaean Patriarchs of Babylon are not to be confused with the Assyrian Patriarchs of Babylon, who derive from Nestorius (but whose current Christology, laid out by Babai the Great in the sixth century, while still not the standard Orthodox picture, is closer to the Orthodox Christology than Nestorius's -- it avoids Nestorius's dualism, although it denies theopaschism, i.e., the claim that God suffered on the cross). The current Assyrian Patriarch of Babylon is Addai II; its traditional list goes back to Thomas.
Of course, I haven't discussed the Oriental Orthodoxy, except in passing. They differ from the above in tending Monophysite -- I say 'tending' because strictly speaking they are usually officially Miaphysite, which is a more vague position, and can be interpreted either as strictly Monophysite or as much closer to Chalcedon. I've already mentioned Coptic Alexandria and Syriac Antioch, which are both examples of Oriental Orthodoxy. The current Catholicos of Armenia (the traditional list of which traces back to Thaddeus and Bartholomew) is Karekin II. The largest Oriential Orthodox Church is the Ethiopian, often called the Tewahedo Church (Tewahedo='being made one', a reference to their Christology), which (of course) traditionally traces itself back as a Church, although not as a patriarchate, to Philip, and is currently headed by (depending on whom you talk to, since there's a split over it) Merkorios or Paulos. The closely related Eritrean Orthodox Church is currently led by its third Patriarch, Antonios. The Malankara Orthodox Church, in India, traditionally traces itself as a church back to Thomas, although not as a patriarchate; its present Catholicos is Thoma Didymos I. (As an autonomous church, it is not to be confused with the older Malankara Syriac Orthodox Church, which is entirely under the authority of the Syriac Orthodox Church of Antioch, and is headed by Catholicos Thomas I, and with which it is still in communion.)
