These are the Hats that you can find in the game. Most of them you find in the dungeons by opening the safes and have to craft them in your home. A Few you get as gifts during a date. These are the 26 hats I have been able to find in game.
Default
Bucket Hat
Headscarf
Turban
Gift
Beret
Blue Flower
Cat Ears
Cool Shades
Designer Glasses
Flower Crown
Headphones
Craft
Bike Helmet
Pretty Ribbon
Bowler Hat
Bucket
Cowboy Hat
Cultist Mitre
Designer Pods
Fox Hood
Halo
Knight Helmet
Lucky Earrings
Phoenix Cap
Royal Crown
Sunhat
Top Hat & Monocle
Valkyrie Band
There is supposedly one more hat. The Baseball Cap but it seems to currently be glitched.