Aspirin was a white crystalline derivative of salicylic acid, which was often used as an analgesic to relieve minor aches and pains or to reduce fever, or use as an anti-inflammatory medication.
When the USS Enterprise arrived at planet M-113 on a supply run in 2266, Professor Robert Crater stated that the only needs that he and his wife had was aspirin and salt tablets. (TOS novelization: The Man Trap)
During an archaeological mission in 2377, Inana Skanda took aspirin for a migraine rather than the native folk remedy, yenara-root tea, preferring a remedy with a track record. (CoE eBook: Remembrance of Things Past, Book I)