Apples: Apple seeds contain cyanogenic glycosides. If you eat enough of the seeds, you could very well die, according to this Mother Nature article.
The real risk is very slight, however, because your body can detoxify small amounts of cyanide, and you'd have to actually chew large amounts of seeds to suffer ill effects. Children and pets are at higher risk than adults.
According to another article on About.com, "symptoms of mild poisoning include headache, dizziness, confusion, anxiety, and vomiting. Larger doses can lead to difficulty breathing, increased blood pressure and heart rate, and kidney failure."
Deadly Nightshade: The nightshade family includes plants such as potatoes, tomatoes, eggplants and chili peppers. While deadly nightshade is the most dangerous, all of these plants contain toxins, usually in their foliage.
Rosary Pea: Rosary peas are traditionally used as ornamental beads. Many jewelry makers have died after handling rosary peas, which contain abrin, a fatal toxin.
Oleander: Oleander is a common garden plant, but ingesting any part of it can be deadly. Even the smoke from a burning oleander can kill you.
European Yew: Nearly all parts of this tree are poisonous. The leaves and the seeds contain a poison called taxanes.
Daffodils: Daffodils are deer- and vermin-resistant, and no wonder -- they have a poisonous numbing effect.
Doll’s Eye: The fruit of a doll's eye plant contain cardiogenic toxins that can lead to cardiac arrest and death.
Hemlock: All parts of the plant contain the alkaloid coniine, which causes stomach pains, vomiting and progressive paralysis of the central nervous system.
Stinging Tree:This plant is the deadliest and most potent stinging nettle in the world. The nettles contain a potent toxin that has been known to kill humans.
Castor Beans: One castor bean contains enough ricin to kill an adult within a few minutes.
Angel’s Trumpet: All parts of these plants contain dangerous levels of poison. People sometimes die trying to create recreational drugs from the plant.
Monkshood: Monkshood was used by ancient warriors to poison the water of their enemies.
White Snakeroot: White snakeroot contains the toxin tremetol. Abraham Lincoln's mother reportedly died after swallowing snakeroot-contaminated milk.