I grew up in a Reform synagogue in which men were expected not to wear a head covering; indeed, in the late 70's, a young assistant rabbi created quite a stir by asking board of trustees permission to wear a kipah ; after a difficult debate, permission was granted. Later, as a teacher at a Solomon Schechter school, I followed the school policy of wearing a kipah for Jewish studies classes and for prayer. From that policy followed the natural decision to wear a kipah from my arrival at school until my departure each day.
But then things began to get weird. As principal of a Solomon Schechter school, I would occasionally go out to lunch at a restaurant with visitors or fellow administrators or lay leaders where I would eat a tuna sandwich or the like, in a non-kosher restaurant. Should I take off my kipah to eat? Should I wear it in a traif restaurant? And what about while driving to synagogue on Shabbat? My own interpretation, and my own comfort level, finally brought me to wear my kipah all the time. Well, almost all the time; not on every flight, or at every sporting event, or shopping expedition, or camping trip. I was consistent in my idiosyncratic inconsistency. I guess my bottom line was that I knew that the covering of the head (or not) was not really very important, as mitzvot go.
Upon making aliyah , I continued to wear my kipah all the time. I soon discovered that by doing so I was sometimes giving off meanings that never occurred to me. For example, there was the time I was working in an archive and declined the offer of a cup of coffee by the librarian (because I didn't want any coffee at that moment), only to have her run out to buy plastic cups and return triumphantly with a cup of coffee that I would be able to accept. Or the times people apologize for disparaging what they assume are my views on such topics as the settlements in the territories, or religion and state, etc.
Moreover, I had to learn the language of kipot :
Black velvet high dome ultra-orthodox
Black velvet flat dignified, moderate modern orthodox
Crocheted, large (over about 5 inches diameter), mostly white with some decoration West Bank settlers or their supporters
Crocheted, bright colors, very large (covering the whole head) born-again, or hippy-religious, or trying to defy definition, or a fashion statement
Crocheted, medium size, very flat, worn hanging at an odd angle modern orthodox yeshivah students
Crocheted, pure white, covering the whole head, with a little tassel at the top Bratslav Hasidim
and the list goes on.
My own choice is the head covering that I associate with a liberal traditionalism in my mind, the kipah of the orthodox kibbutz: crocheted, small (4 inches), somewhat domed, often with a cute design, various colors. Of course, I am not orthodox in my practice or my ideology, so my head covering is the resultant of a few different vectors, including habit, identification, cultural heroes, and probably more factors that I can't really articulate. Clothes make the man, no? And for women, the picture is significantly more complex and interesting