Any purebred dog is at risk for genetic health problems since the gene pool is small. The incidence of health problems in Yorkies has really gone up since they have become so popular. They have become a favorite of backyard breeders and puppy mills. Yorkies are now 36 times more likely to have a liver shunt than all other breeds combined.
The key to getting a healthy Yorkie or any purebred dog is to get a puppy from a reputable breeder who is very knowledgable about genetics and health tests all her breeding dogs. All the parents should have bile acid tests, thyroid panels, orthopedic exams/knee xrayed, heart and eyes cleared, etc. A reputable breeder knows the backgrounds of all the dogs she breeds for generations back and carefully selects her breedings to best compliment the strengths of each dog.
The best place to find a reputable breeder is through the Yorkshire Terrier Club of America:
Yorkshire Terrier Club of America About The Club