Usually cats and houseplants do well once the cats get past the kitten stage. But not always.
My biggest problems with cats and plants has been cats knocking the flowers off cut flowers and blooming indoor plants. I’ve chased more than one around the house with barren flower stalks threatening to turn them into dog food.
Common problems with cats and house plants:
1) The cats use your plant as a litter box.
– Replant the plant and place stones on top. It’ll look pretty and the cats won’t dig through the gravel. A half inch to an inch is fine.
2) The cats eat the house plants.
– I’ve had some but not great success with a spray called ‘Bitter’ you can buy at the pet store. It hasn’t hurt any plants I’ve tried it on and the cats don’t like it. The problem is they don’t know they don’t like till they eat it a few times. Cats are slow learners.
3) Some house plants are toxic to cats. ( see links here for correct information on which plants are toxic to cats ) most are not. Usually the cats leave them alone, but there is no harm in not having toxic plants near your pets. There are lots of non-toxic choices. ( see also ASPCA list of plants toxic to cats )
4) The cats tip plants over. This is my biggest problem. If the plants are not against a window but on a counter or table Fred likes to rub up against the pots and often lighter weight ones tip when he does this. Putting the plants near a window or weighing them down with a few rocks fixes this.
5) Waterbottle training. This has worked with every kitten we’ve had. The first time you see the cat doing something to a plant, spray him with a bit of water from a spray bottle. The second ( or third for slow cats ) time you’ll only need to pick up the spray bottle. I’ve yet to have a cat that needed more than 3 sprays of water to avoid all the house plants. Persist and the water bottle method will work in less than a couple of weeks.