Has there been any marked consumer hat buying trends in the US during
the past 10 years?

Also, can we point to a time when hats became unfashionable and people
stopped wearing them on a daily basis?

Hi flagal,
Wearing hats is not unfashionable, to be precise. It is more a problem
of overdressing -- nobody feels the need for it. Vests are in the same
class. Three-piece suit, anyone?
If you want to talk about unfashionable, see bell bottoms, spandex,
thick chains, et al.
It was through the 50s that hats were still a part of the man's
wardrobe, but with the emphasis on hair in the late 60s and 70s, men
didn't want hats anymore. Hats aren't nice to perfect perms (even on
men).
Another factor in the decline of hat wearing is that hats served to
protect hair from dirt, and in that vein, to extend time between
washings. Now men wash their hair almost daily and drive in enclosed
cars more than walk on dusty streets (and streets aren't as dusty!) so
hats aren't a practical advantage.
Interestingly, hat wearers don't like hair showing under the brim --
so they used shorter haircuts. This also explains why with longer
hairstyles of the 60s and 70s, men didn't like the consequences of
wearing hats.
Basball caps are infiltrating even the most elevated circles,
according to Bernhard Roetzel, and they may be the modern classic that
could pave the way for hats to return.
I found a report on licensed products, a group which many baseball
caps are included in, saying the market hit a plateau, but caps are
stable. Some niche caps, like fitted caps, will even grow in sales.
You can find more details by going to the page:
http://www.sgma.com/press/1998/press985893061-24743.html

Search terms used on Google:
"consumer trends sales baseball caps buying 1990"
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