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
This is possibly my favorite. The way the background of the picture works makes it look like it's slightly cloudy, and the bow in the hair works. Overall, it colors up the picture a bit.
Think! & Ooh, Shiny!