An allergy or allergic reaction refers to a body's inappropriate immune response to various stimuli, usually proteins.
The body's responses can be minimal, but may also include anaphylactic shock or even death. Allergies usually have a genetic basis. They may be present from birth or may present themsleves at any later point during a lifetime.
Klingons are allergic to Tribbles. (TOS: "The Trouble with Tribbles", DS9: "Trials and Tribble-ations")
Joined Trill are extremely allergic to insect bites. The reaction caused by the insect's venom interferes with the biochemical connections between the host and symbiont. (DS9: "The Siege")
Malcolm Reed was allergic to bromelin, for which he took regular injections. He was also allergic to dust mites, oak, pollen, and tropical grasses. (ENT: "Silent Enemy")
James T. Kirk was allergic to Retinax V, an eye medication. (Star Trek II: The Wrath of Khan)
Jadzia Dax was allergic to icoberry juice- it made her spots itch- but she drank it anyway. (DS9: "Let He Who Is Without Sin...")
Tom Paris had an allergic reaction to the water Neelix used for the coffee in a Paris Delight. (VOY: "Threshold")