I've never heard of aspirin held as triumph of modern medical research. Googling "aspirin origins" comes up with a mess of pages that mention both its ancient origins and the modern versions. Even the original patent holder for the modern version, Bayer, mentions use by the Greeks.
Nowadays it seems to pose a problem for pharma industry -- they try to come up with redundant replacements (such as the aforementioned Vioxx) that are patented and don't come $0.99 per 100 pills.
Stories of quinine I found tend to trace back to the Spanish in South America (with faint mention of how they might have found out), but we're still talking about something in use in Europe in the 1600s along with the leeches for black bile -- not exactly a treatment developed by "western science".
-- Andy