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There are probably more kinds of graphs than most people can imagine. A graph is simply a means of conveying information in a visual manner.
Some interesting but unusual graphs are:
Florence Nightingale's study of Crimean mortality. She was one of the early statisticians to grasp the power of graphs.
Napoleon's invasion of Russia.
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Keys, compass, and data
Bar graphs and line graphs.
The answer depends on what information is graphed. There are distance-time graphs, velocity-time graphs, speed-time graphs, acceleration-time graphs.
Bar graphs can compare two sets of data, as well as line graphs and circle graphs. To better improve my answer, double line graphs and double bar graphs compare two sets of data. Circle graphs cannot however, because they compare parts of a whole instead of, as a bar graph would, the amount of something. A circle graph is also incapable of showing data growth over a period of time, as line graphs do. All in all, circle graphs cannot compare to sets of data, and bar graphs and line graphs must be doubled to do so.
Bar graphs and line graphs.