You’re highly unlikely to manage to eat enough apple seeds to poison yourself, so you can rest easy if you occasionally swallow one. Apples contain a compound called amygdalin in their seeds, which is a cyanide-and-sugar based molecule. If the seed is chewed or otherwise broken, human or animal enzymes come into contact with the amygdalin and effectively cut off the sugar part of the molecule. The remainder can then decompose to produce the poisonous gas hydrogen cyanide.

Cyanide toxicity is experienced by humans at doses of around 0.5–3.5 milligrams per kilogram of body weight. Symptoms of cyanide poisoning include stomach cramps, headache, nausea and vomiting, and can culminate in cardiac arrest, respiratory failure, coma and death. A fatal dose for humans can be as low as 1.5 milligrams per kilogram of body weight. In a recent study, the amygdalin content of apple seeds was found to be approximately 3 milligrams per gram of seeds (one seed is approximately 0.7g).

As not all of this mass would be converted into hydrogen cyanide (some of it will constitute the sugar part of the molecules that is cleaved off), it’s apparent that you’re going to need to eat a huge number of apple seeds to succeed in poisoning yourself, and there don’t appear to be any cases of someone having succeeded in doing so.