Beak and feather disease is not contagious to humans but it is deadly to birds affecting their plumage and beaks. It is not curable and can lead to prolonged suffering in parrots especially. The two photographs attached are of Sulphur- crested Cockatoos with this disease.
Giardia is a parasite found in soil and food that can affect humans causing them gastric discomfort or people can be asymptomatic carriers. Down the microscope this bug has two little eyes looking at you.
Chlamydia psitticosis is contagious to cats, guinea pigs, humans and birds. It is a bacteria that causes "bird flu" high temperatures. There are other types of chlamydia as well affecting lungs and urinary tracts.
Thankfully both diseases affecting humans can be treated with antibiotic medicines, it is for this reason that it is important to keep bird baths and water clean (sterile) and to wash your hands well.