Peahat

The Peahat has appeared in many different Zelda games, and has undergone fairly drastic changes in nature over time. It's appearance has always been broadly similar; that of an airborne flower/plant-like creature. The name has occasionally been mis-spelled as Pea Hat (for example in Majora's Mask, see image below). However, the correct official name 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 (see below).

The Legend of Zelda (NES)
In the original Legend of Zelda, they were the spirits of dead flowers, fluttering around the screen, only vulnerable when they stopped moving. The Peahats have only three colours and can not be harmed while they are airborne.

Link's Awakening
Peahats appeared again in Link's Awakening, behaving in the same way as those appearing in the original game. Their appearance was also largely similar.

Ocarina of Time and Majora's Mask
In the N64 Zelda's, Peahats were annoying creatures that sleep in the ground. When you get too close to them, they will shoot up into the air and use their helicopter-like blades to keep themselves in the air. They fly after Link and attempt to chop him down with these very blades. They even send out little baby Pea Hat Larva which are just as annoying. These things are rather hard to kill, so prepare to run as it is much easier.

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

The Wind Waker
Another version of the Peahat is found all around the islands of tWW. To defeat them, you can use your bow and arrows to defeat them in one hit. However, if you don't feel like spending arrows, blow them away with the Deku Leaf and finish them off with your sword--if you don't, they'll grow new "blades". Another method is to hit them with the boomerang twice, very quickly. After they die and turn into smoke, Peahat will sometimes drop a Golden Feather, which is a valuable collectible for a particular side quest involving a Rito sentry.

The Minish Cap
Quote from The Legend of Zelda: 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 Minish Cap (except for a spin attack from the completed Four Sword), but you can suck them in with the Gust Jar which will stun them, allowing you to attack with your sword, or shoot them into walls.

Twilight Princess
It is the first time ever that Peahat don't attack Link, instead they act as targets for the Clawshot to advance over large gaps. There appearance is similar to the Wind Waker version but display roots on it out side. They are mainly found in The City in the Sky where they are extremely important when continuing through the dungeon. They also play an important role in defeating the dungeon boss, Argorok. It should be noted that the Peahats in Twilight Princess can stay aloft when carrying Link, but if he equips his Iron Boots the weight is too great, and they will start descend.