A gentleman should generally remove his hat he enters a building, including a restaurant, home, classroom, theater, church. This rule includes baseball caps and casual hats. Hats are to be removed when inside, except for places that are akin to public streets, e.g., lobbies, corridors, and elevators in public buildings. In public buildings, the elevator is considered a public area, and therefore an area where a gentleman may leave his hat on.
A gentleman should take off his hat and hold it in his hand when a lady enters an elevator in any building which can be classified as a dwelling. He may put his hat back on in the corridor. A public corridor is a thoroughfare of sorts, much like the street, but elevators in smaller buildings such as hotels or apartment homes tend to have the character of a room in a house.
Men should normally remove their hats off indoors, but women do not-- unless it's a rain hat.
The tag that covers the sweatband seam always goes at the back of the head.
For women, dress hats do not need to be removed when indoors. This rule of etiquette has developed out of the role of womens hats as an outfit-specific accessory as opposed to a general one. Where men may have many hats available to match a variety of outfits, women may match only one hat with a single outfit. By a similar rule, womens hats worn strictly for warmth should be removed when indoors.
For men, hats are tipped, (or doffed) slightly lifting the hat off your forehead, when meeting a lady (remove your hat if you stop to talk), or to "say" to anyone, male or female-- thank you, excuse me, hello, goodbye, you're welcome or how do you do. Tipping of the hat is a conventional gesture of politeness. This hat tipping custom has the same origin as military saluting, which came from the raising of medieval Knights face visors to show friendliness.
Men are expected to remove their hats during the playing of the National Anthem. A woman may leave her hat on during the playing of The National Anthem when indoors, unless it is considered unisex like a baseball cap. When wearing such a unisex cap, a woman should follow the same guidelines as for men.
Men's hats are to be removed for the passing of the Flag and funeral processions, outdoor weddings, dedications and photographs.
Removed hats are held in hand in such a way that only the outside and never the lining is visible.
In places of worship head coverings are required for both men and women in Muslim mosques, and Sikh temples.
Men are expected to cover their heads in Jewish synagogues, and married women wear hats or scarves representing a display of increased modesty towards those other than the woman's husband.
The small, round head covering or skullcap worn by men is called a "kippah" which means, "dome" or "cupola". The Yiddish word for the cap is "yarmulke".
The wearing of the yarmulke is a reminder of humility before God, a mark of respect in a Jewish congregation, and a sign of recognition of something greater above oneself, which is why many male Jews wear a head covering whenever they are awake, with the exceptions of bathing and swimming.
It is considered acceptable for women to wear hats in Christian churches, but is sometimes considered disrespectful for men to wear them. A man should remove and hold his hat whenever he is in a Christian church.
For men's hats, any ornaments or decoration on the left side of the hat. The opposite is true of women's hats, hat pins and other ornaments should be placed on the right.