Question:

What will be the status of the gentile nations when Moshiach comes?  Will everyone convert to Judaism?

Answer:

They will not necessarily convert to Judaism, but all will follow the Noachide code.

There are a number of views on this issue found in the Talmud and its commentaries.

The Talmud states that with the future redemption, all non-Jews will return to G-d with complete Teshuva, as the verse states:  "I will transform all nations to a pure language, that all of them will call in the name of G-d and worship Him of one accord." (Tzefaniah 3:9)  Rashi comments:  "It is understood that there will be no difference among (G-d's) servants.  Israel and the nations will all serve G-d in the same manner, with all the mitzvot."

However, Maimonides disagrees with this view.  Although he writes that "all non-Jews will return and do Teshuva," he does not interpret this to mean that they will convert to Judaism.  The non-Jews will all commit to fulfilling the seven Noachide laws that were commanded to all of mankind. 

Maimonides writes thus:  "They... will all return to the true faith.  They will not steal or destroy, but will only eat permissible food, in repose alongside the Jewish nation." The Lubavitcher Rebbe, who analyzes the words of Maimonides very precisely, interprets this passage to mean that the non-Jews will not actually convert and become Jews, but will live peacefully alongside the Jewish people.  In their lifestyle, they will follow the moral and humanitarian principles laid forth in the Torah.