Genetic Modification is an older practice than we usually assume. As far back as 2000 B.C.E., the Ancient Chinese were grafting fruit trees to domesticate apples and cherries. While grafting isn't pure genetic modification -- it allows the plant to naturally assume characteristics based on selection and time -- it founded the basic science. Thomas Hunt Morgan studied heredity by mating fruit flies, generating different groups based on characteristics. Today, with the ability to manipulate individual strands of DNA, genetic modification is much more complex and easier to control.
One extremely harmful and natural genetic modification is caused by mutations in the PrP gene, which creates misfolded proteins called Prions. Prions hijack and misfold proteins in the central nervous system and cause debilitating diseases including Creutzfeldt–Jakob disease and Bovine Spongiform Encephalopathy (mad cow). There is no cure for these diseases, and prions can persist in the environment for many years, since they are not living organisms.
Genetic engineering has been used to create safer Vaccines, which are composed of weakened strains of a particular virus. It is possible to remove the sequences of DNA that cause infection, and so allow the immune system to adjust and prepare for a stronger, infectious strain.