"The novel (and controversial) question of whether or not women may be ordained as rabbis is instructive in shedding light on the process by which the various Jewish denominations arrive at their legal decisions today. Orthodox rabbinic authorities, finding not only no precedent in Jewish law allowing such a practice, but finding sources expressly prohibiting it, have categorically denied women the right to become rabbis. Indeed, the issue is still so remote sociologically and halachically (i.e., legally), that it is rarely ever raised, let alone debated, in Orthodoxy. [new paragraph] Reform Judaism, on the other hand, approaches the issue from a more historical and sociological perspective, with a decidedly liberal approach to the sources or with a flat rejection of their binding authority, and permits the ordination of women. Indeed, there are many female Reform rabbis today. Finally, the Conservative movement, which takes seriously into account the views of Conservative Jews at large and employs a more liberal approach to the traditional written and oral sources than would Orthodoxy, remains divided on the issue, with liberal Conservatives opposing it. Only recently, in 1983, has the Conservative movement decided to ordain women," pg. 47 of "What You Should KNow About Jews and Judaism" by Rabbi Yechiel Eckstein.
Eckstein didn't cite sources for the Orthodox view but here's a few:
"A woman is invalid to serve as a judge" Shulchan Aruch (Choshen Mishpat--C.M.) 7:4
"We may not appoint a woman as king. When describing the monarchy, the Torah employs the male form of the word king and not the female.This principle also applies to all other positions of authority within Israel. Only men should be appointed to fill them," Mishneh Torah (Hilchot Melachim uMilchamot, Chapter 1, Halacha 5)
This is the approach of Paul the Apostle in Scripture: