Obviously Jayne's hat from the Message has got to be the first example, and is probably what set me off thinking about their headgear...
But looking back.
In Serenity (the Pilot)
Cute woobie wash with a cap!
Badger and his "very fine hat"
Poor Two-Fry (it worries me that that name comes to me without even having to think about it) has his hat shot off! Patience has one too.
In Ariel they're all wearing these seriously flattering caps!
Ooooh look more Jayne and hat!!!! he's sooo pretty! Actually he wears a weird hat thing in Jaynestown too *g*
Plus the alliance guys all wearing hats, which seem to be slightly different depending on rank! Yes the hat is a part of the uniform! I don't know why that amuses me but is sooo does :)
I'm sure there must be other examples but i'm late and need to go...
And now i want a 'my fandom is obsessed with hats' kinda icon which is better done that this one *g*