Never give a cat aspirin without the advice of your veterinarian. Cats are unable to metabolize the drug resulting in toxic effects.
Most cats that are exposed to aspirin by either from accidentally ingestion of an improperly stored aspirin or by well-meaning owners giving their cats an incorrect dose.
Don't give your cat aspirin unless directed by your veterinarian. There are some medical conditions in which aspirin is recommended but only as a low dose given every 2 or 3 days.
Aspirin toxicity may cause vomiting, diarrhea, trouble breathing, bleeding problems, lethargy, weakness and/or kidney failure.
For more information please read Aspirin Toxicity in Cats.