The British then forgot why they gave everyone citrus, screwed it up and started getting scurvy again.
There was the cowpox vaccine in 1798
and I suppose we have had effective pain-control (opium) for a very long time
We have evidence of trepanning (drilling holes in the skull) going back to the flint tools time period. We still use this today to release pressure after a bleed in the skull.
The Edwin Smith Papyrus, a papyrus made to treat traumatic brain injury or TBI, is the very first written work made to remedy a medical condition in a way that doesn't depend on sorcery, written around 2000 BC. It gives a detailed account on some but not all do's and dont's of such injuries. I cite this because it actually suggests Egypt knew better than those of us alive today.
I'm not sure if it counts as a cure or more of a prevention, but smallpox was eradicated in 1980 through vaccines!