Yes, there are plenty of pet-safe indoor plants that you can fill your house with without worry.
African violets, Chinese money plants, spider plants, house leeks (sempervivum) and Boston ferns are all safe to bring indoors.
These are quite small and suitable for a table top, but if you are looking for something larger to make a statement in your rooms, you could also consider a banana plant, aspidistra, fan palm or money tree.
Many pet-safe indoor plants are low-maintenance and also help keep the air clean, which can minimize the risk of pet allergies too.