By default there is only one outfit available which is the Tophat. You can unlock various other outfits by completing objectives, defeating the end-boss, or signing up to the Orangepixel newsletter. The various outfits change the starting skills of your character.
Sir #
This is your standard outfit. It has no extra skills or powers, and is the standard way to play the game.
Knight #
The knight is a stronger character and is unlocked by completing 5 objectives. The knight gives you +4 attack and +2 agility and +2 craft.
Wizard #
The wizard hat comes with powerful magic powers, and is unlocked by completing 10 objectives. The wizard gives you +4 magic, +1 luck +3 Alchemy and +1 craft.
Voodoo #
The voodoo mask is unlocked with a secret code. The voodoo mask gives you +2 attack, +2 magic, +1 luck and +2 agility. As a bonus it gives a special skill: Fear.
Skelly #
Skelly is unlocked by defeating the boss. It will give you +3 attack, +2 magic, +4 luck +3 craft and +4 alchemy.