EDIT: Since this post, I've made a more comprehensive post, where I rank every tradable hat in TF2. You can check it out here!
I looked at my website statistics, and discovered that my ancient article calling the Scotsman's Stove Pipe the best hat in TF2 is the most popular thing I've ever written. This is rather depressing, since it's not a particularly meaningful article, and I don't even think it's true anymore.
The coolest hat in TF2 is the Stout Shako. Look at its majesty!
In fact, if you're going to craft a hat, I'd highly suggest crafting a Soldier hat, even if you don't want a soldier hat. Yes, it costs an extra Refined Metal and a Soldier Token, but the Soldier has 4 new hats in the Polycount update, and they're all sweet. You have a 4/9 chance of getting a hat that someone would gladly trade two hats for. Only one of the Soldier hats, the Soldier's Stash, is truly bad. This leaves a 8/9 chance of getting a good hat, far better odds than any other class!
The Familiar Fez is my new favorite Spy hat, but really, all Spy hats are good.
The best thing with Medic is the Otolaryngologist's Mirror plus the Physician's Procedure Mask. It really plays up the medical side.
PS. Does anyone have a Shako to trade?