The following are items that can, in most cases, be found and picked up at any time during the game.
Found once you have the bow, can be used to shoot targets from afar. Picking up one bundle of arrows icon refills 5 arrows in your quiver.
Found once you have the bomb cannon. Used as ammo for the bomb cannon. One bomb icon on the map replenishes 5 bombs.
Pick up a heart to replenish one heart of health. Their rarity will depend on how difficult the enemies are, to balance it.
Small green bottles that replenish an increment of your magic meter. Small jars replenish an eighth. big magic jars replenish it all. Rarity would depend on how many items use magic, and how necessary they are, but fairly uncommon. Rooms with puzzles requiring magic would have pots that have magic jars in them.
Increments found randomly: 1, 5, and 20. Randomly finding a 20 is extremely rare, and those and increments higher than that are reserved for rewards.
Found quite rarely, and sometimes as puzzle rewards. They are saved up for no apparent purpose until you find that they can be traded to upgrade some equipment in a secret out of the way seashell mansion type place.