Cosmetic Armor pieces are designed to be equipped in cosmetic armor slots and commonly don't offer significant stat boosts.
Any wearable armor can be used in the cosmetic slot, provided it's the appropriate type (head, chest, legs, or back).
All cosmetic armor can be collected and displayed on a mannequin.
Hats are cosmetic head piece items. There are a number of in game hats that are player made submissions from the Create-A-Hat forum contest.
Backer Reward Hats
Backers who pledged $500 or more to pre-order the game were granted a hat design to be included in game. The pre-order tier details state; "You get to design a hat for Starbound! Submit a sketch or idea and we'll draw it for you and place it in the game for everyone to find and wear!"
These are the hats that have so far been categorized as backer rewards.
Create-A-Hat Contest Hats
There are a number of player made submissions from the Create-A-Hat forum contest that were announced would be included in the game.
Capes are back slot armor items. Capes don't provide stats, but can sometimes present special abilities such as providing light.
Cosmetic armor sets are groupings of similar armor, usually by name. For the most part, these sets offer no stats, the only value is for appearance.
Biome Cosmetic Sets
Many biomes have unique cosmetic sets that can either be found inside chests, crafted using materials from the biome or sold by a biome specific tenant.
Dungeon Cosmetic Sets
Many dungeons have unique cosmetic sets that can either be found inside chests, or sold by a dungeon specific tenant.
These sets are unavailable through normal gameplay. They may have not yet been implemented, be available only during holiday seasons, intended for NPCs or tenants, or been temporarily disabled. All of these sets are available to spawn in using admin commands