Typically, an immunological reaction to a harmless antigen - the body's immune system mistakenly launches a response when none is needed.

Since this reaction involves all the usual factors; heat, pain, redness and swelling (the body tends to fight fire with fire), the effects can be quite serious, ranging from a sniffle to full blown anaphylactic shock.

some examples:

Hay fever

penicillin intolerance

Nuts

bee stings, wasp stings

a really serious allergic reaction can stop the heart, a situation which can be resolved with an injection of adrenalin, like in Pulp Fiction

I may well be wrong about all of the above. Please do not hesitate to flame / correct me.