Draw multiple squares with ggplot

A variant on your answer, if you want the "background" colors to go all the way to the edge of the graph and not just to the extremes of the data:

ggplot(df) +
  geom_rect(xmin = -Inf, xmax = 0,   ymin = -Inf, ymax = 0,   fill = "red") +
  geom_rect(xmin = 0,    xmax = Inf, ymin = -Inf, ymax = 0,   fill = "blue") +
  geom_rect(xmin = 0,    xmax = Inf, ymin = 0,    ymax = Inf, fill = "green") +
  geom_rect(xmin = -Inf, xmax = 0,   ymin = 0,    ymax = Inf, fill = "yellow") +
  geom_point(aes(x, y), size = 5)

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EDIT: transparency

Adding alpha=0.5 was "working" except for the problem that by using geom_rect, even without referencing the original df data frame, drew a rectangle for each row of df (10 times, in this case). Setting alpha=0.01 shows that there is transparency, but at a 10th the expected level. The approach should have been to annotate with rectangles; annotations draw only a single instance of the geom, not one per row of the original data frame:

ggplot(df) +
  annotate("rect", xmin=-Inf, xmax=0, ymin=-Inf, ymax=0, fill="red", alpha=0.5) +
  annotate("rect", xmin=0, xmax=Inf, ymin=-Inf, ymax=0, fill="blue", alpha=0.5) +
  annotate("rect", xmin=0, xmax=Inf, ymin=0, ymax=Inf, fill="green", alpha=0.5) +
  annotate("rect", xmin=-Inf, xmax=0, ymin=0, ymax=Inf, fill="yellow", alpha=0.5) +
  geom_point(aes(x, y), size=5)

After the comment from joran. The answer:

ggplot(df) +
  geom_rect(aes(xmin = min(x), xmax = 0, ymin = min(y), ymax = 0), fill = "red") +
  geom_rect(aes(xmin = min(0), xmax = max(x), ymin = min(y), ymax = 0), fill = "blue") +
  geom_rect(aes(xmin = min(0), xmax = max(x), ymin = 0, ymax = max(y)), fill = "green") +
  geom_rect(aes(xmin = min(x), xmax = 0, ymin = 0, ymax = max(y)), fill = "yellow") +
  geom_point(aes(x, y), size = 5)