According to the ASPCA, yucca plants are not poisonous to humans, but they do contain compounds that make them toxic to horses, cats and dogs. The toxic compounds are called saponins.
The signs and symptoms of an animal that has ingested the yucca plant can include excessive drooling, vomiting, weakness, incoordination, dilated pupils in cats, depression and diarrhea. The plant has a very bitter taste, which generally makes it unpalatable to house pets, but the plant is more dangerous to grazing animals that are chronically grazing and eat around the yucca. It is unlikely a house pet would tolerate eating enough of the yucca to suffer a life-threatening condition.