Wow did we get way off topic.

And it's Joe's fault
Stiller wrote:So what's the religious answer? actually, I was thinking that the cowboy hat might preclude the need for a yarmulke. Isn't the idea to cover your head in respect? Not that I'm that informed on any theology.
Stiller -
MY ANSWER
it's Judaism - there are answers ... and . . .then there are answers. And nothing really gets answered except with another question. Some of those religious folks have way too much time on their hands thinking about all this stuff. And I'm worried that anything I say here on HAZ might be held against me in a Heavenly Court. I'm going to have enough trouble getting past Saint Peter at the Pearly Gates without some religious comments on HAZ being held against me. Big_Load is right about those meshuginah Fundamentalists in Brooklyn. They view me as a "black sheep" anyway. They never trim their sideburns in their life because of the way one of them translated a Biblical verse about harvesting the fields. Where the Bible says you have to dress like someone from Russia in the 1700's is beyond me. We even get into arguments between leather yarmulkes and cloth yarmulkes. Asking me about religion is sort of like asking George Carlin or Lenny Bruce. In my perspective, the cowboy hat works, but if you have to remove the hat in the Synagogue, you better have a Yarmulke in your holster instead of a revolver.
A RELIGIOUS ANSWER
But as a sincere answer - I'm going to go with Wikipedia:
http://en.wikipedia.org/wiki/Kippah#SourcesThe sources for wearing a kippah are found in the Talmud. In Shabbat 156b a mother urges her son: "Cover your head in order that the fear of heaven may be upon you." In Kiddushin 31a it states, "Rabbi Honah ben Joshua never walked 4 cubits (2 meters) with his head uncovered. He explained: 'Because the Divine Presence is always over my head."
As to the obligation of wearing a kippah halakhic experts agree that it is a minhag (custom). The prevailing view among Rabbinical authorities is that this custom has taken on a kind of force of law (Shulkhan Arukh, Orach Chayim 2:6), because it is an act of Kiddush Hashem. From a strictly Talmudic point of view, however, the only moment when a Jewish man is required to cover his head is during prayer (Mishneh Torah, Ahavah, Hilkhot Tefilah 5:5). (my emphasis)
Even this interpretation is in question; as recently as the 1600s, scholar David HaLevi Segal of Ostrog, Ukraine, suggested that Jewish people should never uncover their heads in order to help distinguish them from Christians — especially while at prayer.
A Hasidic/Kabbalistic tradition states that the kippah reflects several ideas. One is that God covers us with His Divine Palm; indeed, the Hebrew word kaf means either "cloud" or "palm of the hand." The Hebrew letter Kaph is the first letter of the word kippah.
Reasons given for wearing a kippah today include:
Recognition that God is "above" mankind;
Acceptance of the 613 mitzvot (Torah commandments);
Identification with the Jewish people;
Demonstration of the "ministry" of all Jewish people.
Some Jewish people wear two head coverings, typically a kippah covered by a hat, for Kabbalistic reasons: the two coverings correspond to two levels of intellect, or two levels in the fear of God. The Kohen Gadol (High Priest) of the Temple in Jerusalem also used to wear a woolen kippah under his priestly headdress (Chulin 138a).
And the more religious among us wear this one to ensure the Steelers get to the SuperBowl.
http://www.neshomanetwork.com/pistemya.html