The most abundant organic polymers on Earth are cellulose (accounting for ~30% of non-fossil organic carbon), lignin (~30%), hemicellulose, pectin, chitin, and keratin. Cellulose is the most common of organic polymers in the cell walls of plants, which account for most of terrestrial biomass. Altogether, about 33% of plant matter is cellulose. Cotton is 90% cellulose, while wood is about 50%.
Cellulose is famous for being the most abundant of Earth's polymers. Used in every plant, it is excreted by some bacteria as a biofilm. Cellulose is the primary component of cardboard and paper. To produce paper, it is ground into a pulp, bleached, then formed into sheets. To most animals, such as humans, cellulose is indigestible, and is the "dietary fiber" that functions as a bulking agent for our feces. Certain animals, like ruminants and termites, have special bacteria living in their guts to assist in breaking down the cellulose and making it digestible.
Other organic polymers found in large quantities in plants include hemicellulose, lignin, and pectin. These form the bulk of vascular plants and serve different functions. For instance, hemicellulose is non-crystalline, unlike cellulose, consists of shorter molecular chains, and has a branching structure while cellulose doesn't. Lignin makes up a quarter to a third of wood's dry mass, making it the second abundant among the organic polymers.
Not counting plants, the most abundant organic polymers are chitin and keratin, in that order. Chitin forms most of the cell walls of fungi, and the exoskeletons of all arthropods, including insects and crustaceans, both of which are extremely numerous. The amount of chitin found in nature likely surpasses the dry weight of all vertebrate terrestrial biomass. Insects are constantly mass-producing and discarding it when they molt.
Keratin is one of the organic polymers that we are most familiar with, as they make up most of the hard but non-mineralized structures in reptiles, birds, amphibians and mammals. Notably, keratin is the main component of nails and hair in mammals, scales and claws in reptiles, many parts of birds including feathers, and make up arthropod exoskeletons along with chitin.