A number of historicist commentators hold that the number of the beast in Rev 13.18 refers to Caesar Nero -- letters in the ancient world were also used for numerals, and the transliteration of the Greek into Hebrew yields 666.
The big problem with that theory, however, is that Rev 13 speaks of two beasts -- the sea beast and the land beast. It seems clear to me that the sea beast, i.e., the Gentile beast, is Rome. After all, the seven heads would be the seven hills. And since the Gentiles are the water people, Rev 17.1, Is 8.7-8, 17.12-13, Jer 47.2, the beast coming out of the sea would be a Gentile power. The beast who's number is 666, however, is the
land beast, not the sea beast. And the land beast is pretty clearly the beast of apostate Judaism of Jesus' time -- i.e., the Israel of Herod and the high priests. (Related to the imagery -- for example, when Jesus plants one foot on the land and one foot on the sea in Rev 10.2, that means he is Lord of both Jew and Gentile; the land people and the sea people.)
I would take 666 to refer to apostate Judaism -- the number arises most prominently in the pivot in Solomon's reign as Israel's king in 1 Kings 10.14 (2 Chr 9.12-13). The Queen of Sheba has just left and the author reports that "The weight of the gold that Solomon received yearly was 666 talents . . ."
At that point, Solomon begins breaking God's law with a vengeance; he accumulates gold, horses and chariots, and multiplies wives (actually, foreign wives), all actions prohibited in the law (1 Kings 10.14-11.13, Dt 17.14-17). Solomon has become an idolator (1 Kings 11.3-6).
Also, the number "six" is the number of humanity; so the triple six is the superlative, fallen humanity. As Jesus argues repeatedly in the Gospels, so here in Revelation: Israel was not the solution to Adam's sin problem; Israel had become Adam in his sin -- a front for Satan (Mt 12.39-45, 23.13-15, 27, Lk 20.9-19 & etc.).