Yes:
Dust
Hair / fur
Plants, flowers, leaves, grass
Soil
Cotton / wool rags
Most paper and cardboard -> nothing with any sort of plastic coating or stickers
Straw -> not hay
Non-treated wood -> sawdust & wood shaving are examples of this
Algae / pond plants
Garden waste
Noes:
Coal ash
Glossy paper
Litter
Meat-eating animal poop
Diseased/insect ridden plants
Poisonous plants
Cautions:
Dryer lint
Newspapers (due to the ingredients in the ink)
Wood ash -> only not for alkaline soil
Weeds -> no roots / seeds
Evergreens
Manure -> check source, animals with plant-based diets are much better
