Count raster value in a bounding box (spatial extent)

In R, use crop to extract the values and (e.g.) table to count them.

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As an example, let's create a 1 degree grid covering the globe:

library(raster)
x.raster <- raster(outer(179:0, 0:359, `+`), xmn=-180, xmx=180, ymn=-90, ymx=90)

The bounding box is converted to an extent object in order to use crop:

y.extent <- extent(cbind(c(-125,20), c(-60,50)))
y.raster <- crop(x.raster, y.extent)

Having done that, tabulation is straightforward:

table(getValues(y.raster))

In this output the first row lists the values and the second lists their corresponding counts:

165 166 167 ... 257 258
  1   2   3 ...   2   1

As a check we can plot the raster and the extent:

plot(x.raster)
plot(y.extent, add=T)

A minor addition: you could also use (memory-safe) function "freq":

Following the answer by whuber:

library(raster)
x.raster <- raster(outer(179:0, 0:359, '+'), xmn=-180, xmx=180, ymn=-90, ymx=90)
y.extent <- extent(cbind(c(-125,20), c(-60,50)))
y.raster <- crop(x.raster, y.extent)

But now do:

freq(y.raster)

It only matters for very large objects (raster on file). 'freq' returns a two-column matrix (value/count) whereas 'table' returns a table.