That type of graph is called a "heat map" among other terms. Once you've got your correlation matrix, plot it using one of the various tutorials out there.
The ggplot2 library can handle this with geom_tile(). It looks like there may have been some rescaling done in that plot above as there aren't any negative correlations, so take that into consideration with your data. Using the mtcars dataset:
library(ggplot2)
library(reshape)
z <- cor(mtcars)
z.m <- melt(z)
ggplot(z.m, aes(X1, X2, fill = value)) + geom_tile() +
scale_fill_gradient(low = "blue", high = "yellow")
EDIT:
ggplot(z.m, aes(X1, X2, fill = value)) + geom_tile() +
scale_fill_gradient2(low = "blue", high = "yellow")
allows to specify the colour of the midpoint and it defaults to white so may be a nice adjustment here. Other options can be found on the ggplot website here and here.
I have been working on something similar to the visualization posted by @daroczig, with code posted by @Ulrik using the plotcorr() function of the ellipse package. I like the use of ellipses to represent correlations, and the use of colors to represent negative and positive correlation. However, I wanted the eye-catching colors to stand out for correlations close to 1 and -1, not for those close to 0.
I created an alternative in which white ellipses are overlaid on colored circles. Each white ellipse is sized so that the proportion of the colored circle visible behind it is equal to the squared correlation. When the correlation is near 1 and -1, the white ellipse is small, and much of the colored circle is visible. When the correlation is near 0, the white ellipse is large, and little of the colored circle is visible.
You can see the interactive version on my blog. Hover over the heatmap to see the row, column, and cell values. Click on a cell to see a scatterplot with symbols colored by group (in this example, the number of cylinders, 4 is red, 6 is green, and 8 is blue). Hovering over the points in the scatterplot gives the name of the row (in this case the make of the car).
I realise that it's been a while, but new readers might be interested in rplot() from the corrr package (https://cran.rstudio.com/web/packages/corrr/index.html), which can produce the sorts of plots @daroczig mentions, but design for a data pipeline approach:
This is a textbook example for a hierarchical clustering heatmap (with dendrogram). Using gplotsheatmap.2 because it's superior to the base heatmap, but the idea is the same. colorRampPalette helps generating 50 (transitional) colors.