Ball cap for most occasions. Hard to find one that fits just right. Have a small smattering of these (one is required for work).
Knit acrylic/wool
thick stocking cap for cold/ below cold conditions. Have a few (one with work logo).
Fedora for rare occasions, black wool. Matches my trench coat and pea coat nicely, warm, stylish.
Bowler for extremely rare occasions. I look awesome in it and have worn it exactly once. And no, not with a wifebeater, sports jacket, and tie.