This has generally been in the form of wood shavings, usually cedar. This was very very wrong. Do not use cedar for bedding for rodents. It contains some very strong oils, which provide the cedar scent that masks the smell of the cage. However, these volatile oils can also irritate the skin and eyes of many rodents and possibly even cause permanent damage or death.
Some people say the same thing about pine shavings, which also contain some volatile oils.
I have found the animals prefer the aspen chips. I have found that Care-Fresh seems to absorb odors better. You want the chip type. I have heard reported, but never seen, negative reactions to pine among rats and gerbils. Corn cob, often used for birds, isn't very absorbent and is hard for animals to make nests in because it shifts too much.