The Cooperative Collections are properly known as "Community Collections."
Introduced with the Mondain's Legacy expansion, Cooperative Collections are a way for players to contribute for a common cause. Each collection has different items for donation and gives different rewards. The collections are mirrored on both the Felucca and Trammel facets, each independent of the other for tiers and personal donation points.
In 3 places in the game, the Britain Library, the Vesper Museum, and the Moonglow Zoo, players can achieve rewards, including certain artifacts and various decorative items, through making contributions to the location.
The contributions accepted always relate one way or the other to the location. For example, the Zoo takes animals, the Museum wood, and the Library books. (Not exclusively, those are just examples.) All of the locations take gold.
Players achieve individual rewards through donation. For the most part these individual rewards are linked to the location. For example, library rewards include powerful talismans named after famous in-game books, zoo rewards include Luck armor, and museum rewards include items named for famous personalities or fixtures from the game's history (an artifact kryss named for Lord Blackthorn for example).
Also, as more and more people contribute the location becomes better stocked and more pleasant to be and look at. More exhibits in the museum for example, and more animals in the zoo. Donations accumulated by each location decay over time. So, for example, during the Ophidian invasions of Vesper, museum donations dropped off, and the exhibitions of the location declined precipitously.
Britain Library Collection - Located outside Castle Britannia, this collection has many different representatives to donate to. Each representative takes different items related to their section, such as a Book of Chivalry for the Paladin and a Treasure Map for the Treasure Hunter. Notable rewards include history books that talk and the Reading Glasses.
Moonglow Royal Zoo
Moonglow Royal Zoo Collection - Located south of Moonglow city, this zoo displays many exotic beasts of Britannia. Rare and almost extinct creatures can be found inside. Donors can be rewarded with creature statues to decorate their house and royal zoo armor.
Vesper Museum Collection - This collection can be found on the southeast most portion of Vesper city. Donations pay for exhibits that display the known history of the world. Different types of wood are the most popular donation. Donors can receive talking statues and replicas of famous weapons or armor.