When there are two categorical variables it is common to make a stacked barchart. The stacked barchart primarily allows the reader to see the overall count, but it is harder to compare the counts of categories, the colored segments. Using data from the vcd package in R, here is an example. The data describes the responses of couples on questions about their sex life.
This is a bar chart showing the husbands views, with his wifes’ views forming the stacking.