Peahat

The Peahat is a common enemy that has recurred over different Zelda games. Generally it has kept the same form, but its behavior and functions have changed drastically over time. It resembles a flower/plant-like creature, similar to a pineapple or bush, with leaves either at its base or top that function as helicopter blades, making it flight-capable.

The correct typography is Peahat, as confirmed by the official website, the manual for The Legend of Zelda , and the in-game Figurine Gallery of The Minish Cap. Pea Hat was used in Majora's Mask.

The Legend of Zelda
They are the spirits of dead flowers, fluttering around the screen in packs. They appeared in red, blue, and orange, and fluttered about the screen immediately when Link came upon them. They can only be harmed when they stop moving. Then they are vulnerable to the sword, arrow, or bombs. They are resistant to fire and the boomerang, even though they would be stunned by the boomerang.

Link's Awakening
Peahats returned and behaved in the same exact way as in The Legend of Zelda, but only came in one color.

Ocarina of Time & Majora's Mask
In Ocarina of Time, Peahats got a major overhaul. They grew to ten times the size of Link, moved their blades to their base, and became solitary creatures. They were only seen in the southern and northern corners of Hyrule Field, away from the paths and crossroads, making them encounters with them uncommon. During the night, they slept buried in the ground, only revealing the blossom on its top. During the day, they emerged. Only one Peahat is found in Majora's Mask, in a hidden hole in Termina Field.

Their behavior also became more passive and calculated, rather than randomly flitting about. When approached, it shoots up into the air and hovers over Link using its helicopter-like leaves to stay aloft. Then it will either spout Pea Hat Larva from its blossom which buzz around Link like insects and attack,[The master peahat is the only peahat that does this.] or it will swoop down and attack him with its blade-like leaves. If attacked at night, it will only spout Pea Hat Larva, and not emerge.

Its vulnerable point is the root, so a well-aimed shot at its bottom with a slingshot or bow will take it out. Its spinning blades make it invulnerable to a sword or other melee attack.

It is confirmed to be the only creature in Ocarina of Time capable of dropping two different types of loot at the same time, although it does this on an uncommon basis.

Oracle of Ages & Oracle of Seasons
Peahats in the Oracle games are almost identical to those from Link's Awakening, and are defeated in the same manner.

The Wind Waker
Peahats are found all around the islands, but congregate in the Forbidden Forest. They are smaller than they were in Ocarina of Time (see also: Seahats). They are more aggressive, and come in packs of about two or three.

Their helicopter leaves have migrated to the top of their bodies, and they use these to defend against sword hits as well. The bow and arrow will defeat them in one hit. Their leaves can also be blown away by the Deku Leaf, or the Hookshot, leaving them vulnerable to melee attacks. If left alone, they will grow new leaves. The boomerang can also stun them with a double-hit. Upon defeat, the Peahat will sometimes drop a Golden Feather, an item for the Spoils Bag which is a valuable for a side quest involving a Rito sentry.

The Minish Cap
Quote from The Minish Cap Peahat figurine:

"Appears on Mount Crenel, etc. These strange beasts hover on propeller-like leaves. You can pull them out of the sky with your Gust Jar."

They are impossible to hurt with your sword in The Minish Cap (except for a spin attack from the completed Four Sword), but you can suck them in with the Gust Jar or throw your Boomerang at them which will stun them, allowing you to attack with your sword, or shoot them into walls.

Twilight Princess
In this incarnation, Peahats have ceased to become an enemy and are now a tool, or helper for Link. Their appearance is similar to The Wind Waker, but with a more realistic appearance. Their bottom root is more sac-like, resembling a burlap ball, or a cactus.

They float in the sky, and are invulnerable to any weapon. Their only purpose is to act as targets for the Clawshot to advance over large gaps. Mainly they are found in either the Gerudo Desert, or the City in the Sky (where they play an extremely important role in progressing through the dungeon). These Peahats stay aloft when carrying Link, but if he equips his Iron Boots the weight is too great, and they will start descend.