Irwin Mortman answered:
>It is my understanding based that the head covering did not become a minhag
>until the Jews were exiled to Babylon. Supposedly to separate the Jews from
>the rest of the community.
Jews were always required, according to Halacha, to have their heads
covered at the time of Davening (Prayer) (at least by means of Talit),
when entering a Synagogue or when reciting a blessing, as a sign of
respect and reminder that G-d above him and watching him. The term
"yarmulkah" is a combination of the 2 words Yirah MayEloka - the fear of
G-d. When one wears a head covering, he displays a respect for G-d. He
shows that he is aware that there is a Being above him.
According to the Talmud, it was prohibited for any 'faithful' Jew to
walk around anytime with an 'uncovered head'. Traditionally, therefore,
Jews always had their head covered at all times.
The Talmud in Shabbos 152b relates that the mother of Rav Nachman bar
Yitzchak was told by astrologers that her son will grow up to become a
thief. She made sure to keep his head always covered and would tell him
"cover your head so that you will have the fear of heaven". The Talmud
in Kiddushin (33) also comments regarding a person who did not cover his
head "how arrogant is that person". (See also, Tractate Shabbos 118b;
Kiddushin 31a; Shulchan Aruch Bais Yosef, Orech Chaim, Chapter 91;
Rambam Sefer HaYad, Hilchos Dayos, Chapter 5:6; Moreh Nevuchim Part 3,
There _is_ yet another aspect mentioned in many books, that since it is
somewhat of an established custom amongst non-Jews to keep their head
uncovered as a sign of respect (as we see that in courts and other places
one is required to remove their hats) there is the law of "and in their
statutes (ways) you shall not follow" [i.e. don't duplicate non-Jewish
practices], resulting in the Minhag (custom) of actually wearing a Yarmulka
(Kipah) at all times.
It did start out as a tradition to have one's head covered at all times
in one way or another (i.e. hat, Talit, etc.), which later became a
Minhag to where a Kipah. As such, wearing a Kipah is the accepted
practice and law, brought in Shulchan Aruch (Code of Jewish Law).
Yosef Y. Kalmanson