This morning Banshee Legend asked me for a hat, that is it above, and when I saved it into the Twitter Hats folder I realized it was the 475th Hat. That is a lot of hats! You can see them all on the Twitter Hats page.
I started putting hats on my own Twitter avatar in June, 2011 as a form of protest over the high-priced Monocles and other clothing items in the Incarna store. It wasn't long before other Tweetfleet members started asking me to put hats on their avatars. During the time when CCP took away the Frills on the new Vagabond, we even started wearing Victorian Frills around our necks as a form of protest. Which helped to bring the Frill back to the ship.
Over the years since I still get asked for hats, it usually happens in cycles from time to time. There is something to seeing your Eve Avatar wearing a hat. This cannot be downplayed, it has a magical quality to it.
Hats will probably never appear in-game, at least not in a way that breaks the fictional universe allowing for "cowboy" hats or "caps" on our avatars. But that doesn't mean it wouldn't be awesome!!
Until then I'll keep popping them on avatars. Just for the fun of it.