Common parasites spread by pests can include tapeworms; in tropical areas mosquitoes may spread filarius worms.
Fleas are a familiar parasite. The most common flea we encounter is the cat flea, which also infests rodents, dogs, and other animals. While the cat flea can carry diseases and parasites, it is the rat flea that is the vector for Plague. Plague in the United States has established itself in rodents in the Southwest. Each year about 25 cases of Plague are reported in the US.
For more information on parasites, visit the CDC.