I'm trying to find data on the breakdown of the popular vote in each U.S. county, for each presidential election going back as far as possible. I realize that counties change over time, but are these data available somewhere?

For example, I'm trying to find the data behind this map:

for as many presidential elections as possible. Obviously going back decades means that not all of these states existed (as states) at the time, but I'm still hoping the data are available.