Houseplants that are safe for pets include African violets, orchids, spider plants, Christmas cactus, bamboo, African daisy and alyssum. If an animal ingests these plants there will be no negative side effects, except for a possible upset stomach.
There are thousands of nontoxic plants that animals can be around. African violets are a common houseplant and does very well indoors with good sunlight. The deep purple flowers give a great splash of color to a home. The violets that can be found outside in some yards are also safe for pets to be around. Violets can actually be candied and eaten even by humans.
Despite their exotic appearance, orchids are nontoxic to both cats and dogs. These plants are often inside plants because they need to be kept warmer than plants that can be placed outdoors. They also need good sun, which means windows and cats love to lay in windows to sun. If the cat gets curious and takes a bite, the plant won't harm the animal at all.
Bamboo is popular to grow in pots and set on home desks to liven up work areas. This means that these plants will be in areas heavily trafficked by animals. Being wood, bamboo can be tempting for dogs to chew on or for cats to nibble its leaves. These plants will not hurt your pet and the plant will likely bounce back from the damage easily.