Here are some of my favorite hats/ones with interesting stories. For a full list of my hats, see revision history.
This one was interesting - the question I asked for this hat unexpectedly hit HNQ, and it's now my top-voted question on the network... and I also posted a late self-answer to it that got 50+ upvotes and the Sherlock hat, none of which I had intended to happen when I asked the question (I had expected it to not go higher than 10).
Hat combo time!
Think! & I'll Handle It
Think! & Some Kind Of Sun Thingy
Think! & Ooh, Shiny!