The number of the beast
The number of the beast — 666 or the manuscript variant 616, and the identification: Nero, an empire, or a figure still awaited.
Revelation 13:16-18
16He causes all, the small and the great, the rich and the poor, and the free and the slave, to be given marks on their right hands, or on their foreheads;
17and that no one would be able to buy or to sell, unless he has that mark, which is the name of the beast or the number of his name.
18Here is wisdom. He who has understanding, let him calculate the number of the beast, for it is the number of a man. His number is six hundred sixty-six.
What each tradition says
Rabbinic / Midrashic
Ginzberg writes that Jewish bitterness against Rome from 30 to 130 left no conception except that Rome’s ruler would gather the heathen hosts for the final struggle and lead them to victory. Nero, the vilest wretch ever enthroned, filled the ideal of wickedness and was considered the worthy leader of the heathen.
Louis Ginzberg, in Isidore Singer (ed.), The Jewish Encyclopedia, s.v. 'Antichrist' (New York: Funk & Wagnalls, 1901-1906) — Antichrist, section 'Nero as Antichrist'
Patristic
Irenaeus holds that reason leads to the conclusion that the number of the beast’s name, when reckoned in the Greek mode by the value of its letters, comes to six hundred and sixty-six. He states that the tens equal the hundreds, and the hundreds equal the units.
Catholic
The Catholic Encyclopedia observes that long efforts to decipher 666 with the Greek alphabet, including Irenaeus's, yielded no satisfactory result. Using the Hebrew alphabet had better success: many scholars concluded that Nero is meant, since spelling "Nero Caesar" in Hebrew letters yields 666.
Christian van den Biesen, The Catholic Encyclopedia, vol. 1, s.v. 'Apocalypse' (New York: Robert Appleton Company, 1907) — Article, section on chapter 13 (the number of the beast)
Orthodox
Hippolytus urges that we should neither give the name out as certainly his, nor ignore that he may not be otherwise designated. Keeping the mystery of God in our heart, we should faithfully keep what the blessed prophets told us, in fear, so that when these things come to pass we may be prepared and not deceived.
Hippolytus of Rome (c. 170-c. 235), Treatise on Christ and Antichrist (trans. S. D. F. Salmond), in Ante-Nicene Fathers, vol. 5 (Buffalo: Christian Literature Publishing Co., 1886) — §50 (on the number of the name)
Reformed / Protestant
Matthew Henry states that the beast’s number is given in a way showing God’s infinite wisdom and fully exercising human wisdom and accuracy. It is the number of a man, computed in the usual manner among men, and it is 666.
Matthew Henry (1662-1714), An Exposition of the Old and New Testament, vol. 6 (Acts to Revelation), on Revelation 13 — Comment on Revelation 13:18
Evangelical
Albert Barnes states that this number is correct, though in Irenaeus’s time some copies had the other reading, 616. He notes that Tychonius adopted 616, and that Irenaeus spoke against this reading.
Albert Barnes (1798-1870), Notes, Explanatory and Practical, on the New Testament: Revelation (New York: Harper & Brothers), on Revelation 13:18 — Notes on Revelation 13:18
Evangelical
John Nelson Darby states that it is Antichrist, the false Christ of Satan, who subjects the earth to the Satanic Roman Empire. The cited position identifies Antichrist as the one who brings the earth under that Satanic empire.
John Nelson Darby (1800-1882), Synopsis of the Books of the Bible (London: G. Morrish, 1860; complete-scan 'Hodgett' edition) — On Revelation 13