Some plants can be very harmful to cats.
Ivy, Tulips, Yuccas, Lilies of the Valley, and Pointsettas contain poisons that lead to nausea and vomiting. The berries of mistletoes and hollies may cause collapse. Dumbcane and heartleaf will irritate the mucous membrane. Cyclamens, oleander, snowflakes, daffodils and snowdrops are highly poisonous, and may even be lethal. Contact your vet for a complete list of toxic plants.
If you suspect a poisoning, take your cat to the vet immediately.