Speaking from our experience with our Yorkshire terrier Harry, they will normally not have any problems accepting other pets. Being a terrier it will naturally want to check out any other animal it is unsure of, but this is due mostly to curiosity.
Generally they will accept cats that live under the same roof, but have been known to chase any neighborhood cats. Our Yorkie however does not even chase these cats. Harry gets along well with all other animals although he is prone to get very jealous if all attention is not on him.
One thing that should be noted is that Yorkshire terriers must never be left alone with other smaller pets like, hamsters and birds. You must remember that it does have a hunting nature and this could cause it to go after a smaller pet and believe it to be prey.
When it comes to yorkshire terriers and other breeds of dogs, they are smart dogs and will normally recognize the dominance of a larger dog. It is very likely that they will establish good relationships with other dog breeds.
When Harry came into the house he met Tasha (black Labrador) and they get along just fine.
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