Most of special items in the game, once collected, will appear on the far right of the pause menu (rucksack screen).
These include:

Weather Vane
Flower Card: For every 10 points you can pull a lottery ticket.
Cake Card: For every 10 points you may pull on lottery ticket.
Treasure Map: Leads you to Music Box, found in the tree on your farm.
Music Box
Book
Medal Bag: During the dog and horse races, you can bet on the competition. Once you have some medals, you will have this item.
Gold milk
Old wine

Other items:
Use the Ocarina to play music.
The Rug has a nice design and is used for decoration.
The Cupboard can be used to store flowers and milk.
The Tool Box will hold your tools.
The Blue Feather is an engagement item.