A head-covering increases one's awareness and awe of Heaven: Shabbat 156b; Kiddushin 31a
Not travelling 4 Cubits with one's head uncovered: Shabbat 119b; Kiddushin 31a
That important people should wear head-coverings: Kiddushin 8a
That Torah Scholars should wear head-coverings: Kiddushin 29b, 30a
That married people wear head-coverings: Kiddushin 29b
General mention of wearing a head-covering in public: Nedarim 30b; Kiddushin 30a
Minors and head-coverings: Nedarim 30b
Wearing a head-covering before a Torah Scholar: Kiddushin 33a
Covering one's head when visiting the sick: Nedarim 40a