Modern medicine has only existed for the last century or so. Before that the diseases that killed people were more exotic than things like the common cold, which the inhabitants of the Northern hemisphere had become resistant to. True enough diseases like plague and Spanish flu ravaged the populus, however there was always a natural equilibrium reached as the disease killed too many people, it had no vessels to spread to, burning itself out.
The real danger from a alck of medicine would not be disease, but infection. A simple cut or graze could become deadly if not kept clean, which was very difficult to do before antisceptics were invented.
It depends on what you mean by without medicine - the modern population of the world would definitely be not able to cope without medicine, and I'm pretty sure that a good, solid percentage of people would be wiped out effective almost immediately, with alongside the entire "civilized" world soon following.
But if you mean Earth evolving without medicine altogether, the situation wouldn't be so bad - there'd be much less of us to begin with, and we'd be a lot more hairy.
The thing is, the vast majority of the Earth's population either has severely limited access to medicine, or none at all. In addition, for the vast majority of mankind's existence there has been no real medicine to speak of. Things would be much worse than now, sure, but it wouldn't be the end of the world as some of you are making it out to be.
