While I can't say quite when it was fully phased out, it probably started with Andreas Vesalius's findings. Vesalius still studied under the Galenic method, which included the existence of the four humours, but would soon set out to prove some of Galen's medical science totally incorrect--for example, he found that humans had one, rather than two, jawbones, and made numerous discoveries relating to the cardiovascular system. As a result, it's likely that his initial questioning of Classical methodology (as was characteristic of the Renaissance) was the beginning of the end for the humours theory.