There is no Torah or rabbinic requirement to wear a hat. None. No halachic authority says you should wear one to a wedding, funeral, siyum, shul meeting, school event, or any of the other places I've seen them. A (bad) case can be made that you're required to wear them during davening, but this obligation (if it exists) can certainly be discharged with a talis; anyway, as I've said, the case that any sort of additional head covering is required during davening is really quite amazingly poor; besides, it wouldn't be a black hat, per se, that's required. Any style of head gear - from balmoral to pork-pie - would be okay.
So why do we Orthodox Jews make a fetish out of the black hat? Fear and insecurity, mostly: Fear of neighbors, fear of change, fear of being different, fear of sticking out, fear of seeming "less frum", fear of making (or of being seen to have made) an unauthorized break from the so-called grand and so-called glorious past. Put on a black hat, and all those fears are instantly mitigated. With the big black hat on your head, you're suddenly in uniform, part of the crowd, and in intimate fellowship with history and community; even better, you can tell yourself the sweet, sweet, reassuring lie that you've just done something authentically and legitimately Jewish. What an easy way to please God! What an easy way to broadcast your frum bonafides to the neighbors! What an easy way to fit in!
Of course, the man in the hat is to some extent fooling himself, but the real problem is that to a large extent he's not. Black hats have been part of the official Jewish uniform for little more than half a century. God (I hope) doesn't care what you put on your head, but the frum community really is more accepting of men who wear black hats. Hat wearing men extend a certain chumminess to each other, and tend to feel more comfortable socially with other men who wear hats. Those of you familiar with old-style WASP country club rituals will recognize this: Newbies who showed up in the right blazer, and the right set of slacks could expect a better welcome than those who did not.
We can agree, I hope, that putting a chunk of shaped felt on your head doesn't elevate you in any way. With a hat or without it, you're still the same tzadik or rasha. Unfortunately, the slow and stupid of Israel don't see it this way. Boys who wear hats are thought to make better husbands, and better students. Hat wearing Rabbis tend to confer more respect and extend greater deference to hat-wearing congregants. For the slow and the stupid the presence of a hat is a handy shortcut. If you have one on your head you're in; if you don't you're something else, and often something less.
To use clothing this way is human nature, of course, but aren't Orthodox Jews supposed to be better than human nature? Aren't we called upon to transcend or to defeat the worst part of ourselves -- and don't we, sometimes, point with a little too much glee at how other communities fall short? So why does the Orthodox Jewish community, as a whole, accept and reinforce the black hat sham? Is it expecting too much to insist that we judge people on something more tangible than headgear? Or are Orthodox Jews just kidding themselves when they look down at other communities?
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