The American Society for the Prevention of Cruelty to Animals (ASPCA) lists lilies, tulips, azaleas, yew and oleander as poisonous plants. There are many more and some are specific to either dogs, cats or horses.
Lilies are very toxic to cats. The ASPCA has not been able to narrow down and figure out exactly which component in the plant causes illness. In cats, the plant can cause severe kidney damage to the animal. With tulips, it is the bulb that is poisonous. The ASPCA doesn't specify an animal that it affects so it can very likely affect cats, dogs and horses. If an animal ingests the bulb, it may suffer from drooling, loss of appetite, depression of the central nervous system and convulsions, among other symptoms.
Azaleas are a woody blooming bush, mostly found in yards, which can make it hard to protect pets from it if they wander around freely. These plants contain grayanotoxins, which can cause a pet to suffer from vomiting, drooling, diarrhea, weakness and depression of the central nervous system. This plant can kill animals if the ingestion of it is high enough. Death from azaleas normally occurs due to cardiac collapse. Yew contains taxine, which can cause issues with the animals' central nervous system, which can show as shivering, trembling and difficulty eating. Yew can also cause cardiac and gastrointestinal failure which can lead to death.