(Why are people talking about caps when the question was about hats?)
I wear a hat because I like it, and it looks good. My comfort-zone is what could best be described as business casual. I have t-shirts, but I very rarely wear them, preferring button-downs, jeans on the weekends. The hats I have (fedora or flat cap, depending on the weather and my mood) complement my style perfectly.
OTOH, my hair is thinning in the front, and I’ve got a 50-cent piece sized “crop circle” on the crown, but that doesn’t play into my decision.
Why do some people obsess over other peoples’ clothing choices?
A cap is not a hat?
There you go assumpting things; when I said hat I meant hat.
https://www.nouilles.info/illustrations/sdmb_portraits/68402.jpg
Actually that one of its two black cousins are my main ones. I will go with a ball-cap now and then but ----- that face was made for something that sticks a fer piece past my ears. 
(Plus another advantage is that when I do wear it indoors people assume I’m some sort of religious nut and avoid me. I like being avoided in public.)
Anything without a full brim all around is a cap; to most people. We had a long drawn-out discussion of that at a Ducks Unlimited meeting once. Don’t ask – it didn’t even make sense at the time.
*“A cap is a hat,”
He said as he sat.
“Whether crowning a rat
Or me, a big cat.”
“Why care what they wear?
Perhaps they’re sans hair.
Or shielding themselves
From the sun or cold air.”
“Some hats just look nice,
But be sure to think twice
About wearing another’s.
It could give you lice.”
The cat then revealed
His own fancy hat.
Red stripes on white field,
And my head he did pat.
“Whether bowler, fedora,
Tricorn, or pork pie.
A trilby or cloche,
I’m not gonna lie.”
“A hat can be useful,
Or worn just for fun.
Of cotton or sheep’s wool
Just wear one, my son.”*
Ok, but if it’s a cap is it not still a hat?
Sometimes it’s a good thing too. One co-worker I’ve known for years always wears a ball cap hat: the few times he takes it off reveals a head that seems lumpy/mis-shapen, exacerbated by his close cropped hair. When he takes it off, my first reaction is an unspoken “dude, put the freakin’ hat back on”.
A hat is like shoes. There are some situations where it’s okay to go outside bareheaded, but not very many. And why would you want to?
You are correct, sir!
Why are you on a message board whose motto is ‘fighting ignorance since 1973’?
Look around, most people don’t wear hats. And yet, some people wear them all the time. Inquiring about that isn’t obsessing, it’s called being inquisitive.
I’m an old, bald dude and I have to be careful to wear a hat on sunny days (in fact, I prefer an obnoxious cowboy hat to ensure excellent sun protection), but I don’t wear them at my desk, at the dinner table or at everyday functions. It’s odd to wear a hat all the time and I, too, am curious why some people (although, this does seem to be primarily a male thing) wear hats all the time, even when sunburn is impossible.
I don’t think the OP is wondering about you folks who wear a hat to protect yourself from the sun. I think we can all see that wearing a hat under those conditions makes sense, it’s the folks who wear them constantly, regardless of the weather or if they’re indoors or out.
Thanks to those who have replied with their own experiences. It seems thus far to be a number of reasons:
-I like to wear them
-I feel like I look better/younger with one on
-I don’t have to worry about how my hair looks
Sometimes, that is a factor. One factor in why I keep my hair completely covered is that I like having that additional barrier separating me from people.
You look good in that photo.
The suspenders with that hat is why folks leave you alone. You look like a Mennonite or some kin to them. Most folks do not want to be “bothered” by “religious” folks.
IME, Mennonites are skilled craftsmen & craftswomen who can not force themselves to do shoddy work. I enjoy their company.
It is unusual for me to actually laugh out loud, but this post did it.
Summer: Tilley-like sun hat
Fall and Spring: transition to wool watch cap
Winter: balaclava with liner
I lead an outdoor life, there are few days that some kind of hat isn’t useful. I do not wear a hat indoors except in my own house in winter. We don’t heat it to American temperatures.
I think men who wear ball caps look slovenly, unless they are actually farming at the time.
I am not a head-covering-name-Nazi but --------------- no. I am told the argument goes back as far as colonial days with the differentiation between workmen’s caps
which were legal in certain situations and not others; along with the various hide caps (like the cookskin cap on the top of Old Dan). Anything short of full brim and it is a cap and NOT a hat.
I like most of the various folks I’ve known among the OOD and off-shoots.
It’s funny but even when my entire dress is full-blown English the hats still work. There is something about a “plain hat”/kepfa that, even with children, says “that ain’t Santa”. Especially since the Fat Guy himself is almost always depicted in a cap of one kind or another. Don’t know; never really studied the psychology of it all ----- but it works for me. But if I switch to a ball-cap ----- all bets are off.
Keep telling that to yourself… no matter what everyone else says. 
Interesting, but unconvincing. Caps are still hats to me. I can go along with the definition that hats without a full brim are caps, but caps should still be a form of hat.
Umm, it’s madam, not sir.